The simple answer is that Model Ms and their membrane flavour of buckling spring key-switches were conceived as an overall cost-saving compared to the Model Fs and their capacitive buckling springs, but does this actually matter? Are Model Ms without merit? This page will summarise the core differences between the two keyboard designs and attempt to review three specific points of comparison to help you decide which one interests you or suits you the most. Due to the wide variance within both these two juggernaut keyboard families, certain members of the Model F and M families are in mind during this comparison:
More information: Model F keyboards (coming soon) & Model M keyboards
The Model F was IBM's designation for its primary keyboard family of the first half of the 1980s, famously shipping with the original IBM PC in the form of the IBM Personal Computer Keyboard (typically referred to as the Model F/XT) and later joined by a wide range of terminal variants. The next most common variant is the IBM Personal Computer/AT Keyboard (aka, the Model F/AT). All Model F keyboards employ the original capacitive implementation of IBM buckling spring switches.
The Model M was IBM's designation for its primary keyboard family from the mid-1980s to the mid-1990s. Model Ms saw much wider adoption across the board than Model Fs, resulting in a great number of variants that are impossible to all consider at once. The two most famous variants are the full-size IBM Enhanced Keyboard (aka, the standard Model M) and the tenkeyless IBM Space Saving Keyboard (SSK). A sizeable majority of Model Ms employ the cost-saving membrane version of IBM buckling spring switches but it should be noted that another sizable portion uses alternative key-switch designs such as IBM buckling rubber sleeve and IBM Quiet Touch rubber dome switches.
More information: IBM buckling spring
The main succinct difference to discuss between the two keyboard designs is their key-switches. Model Fs use capacitive buckling springs that feature a buckling spring assembly - itself compromised of a pivot plate (also known as a hammer, rocker or flipper) and a coil-spring - that rocks over a capacitance-sensing PCB. When you press a key with such a switch design, the pressure causes the coil-spring to catastrophically buckle in a way that pivots the pivot plate to rest atop a capacitance-sensing pad on the PCB underneath, registering a key-press in the process. The use of capacitance sensing allows for N-key rollover (NKRO) and a high expected lifetime of approximately 100 million key-presses.
Model Ms that have buckling springs use the membrane buckling spring variant. How the switch mechanically rocks is unchanged, but the sensor is completely different as it uses a dual membrane sheet sensor instead. Contrary to popular belief, a membrane is not a rubber dome key-switch design as it purely describes a plastic circuit that has traces silk-screened on them. For this design, the catastrophically buckling spring pivots the pivot plate to apply pressure on the membranes to bridge a contact trace on each sheet together. Due to the lack of capacitance sensing or the ability to fit diodes into the design, Model M membranes are limited to two-key rollover (2KRO) and only rated for a lifetime of approximately 25 million key-presses.
The buckling spring assemblies themselves also differ slightly as the capacitive variant's spring has more coils in its coil-spring and has a larger pivot plate. These differences change the feel and sound between them. Capacitive buckling springs are best described as feeling smoother and lighter and have a more high-pitched and pingy sound, whereas membrane buckling springs feel heavier and more 'baritone' by comparison. That said, membrane buckling springs still have a considerable amount of ping and both designs are considered to be smooth feeling switches with a unique tactility that has no real analogue outside of IBM and its divisional descendants.
TLDR: The Model F's buckling spring implementation is technically superior and generally feels smoother, but the feedback properties are something subjective and it's not unheard of to find people who prefer the Model M's heavier and deeper sounding buckling springs.
The Model F's outer casing is typically a hard plastic (believed to be polycarbonate) with some variants sporting a metal bottom case piece (F/XT) or even fully metal cases (IBM 4704 keyboards). The hardness typically makes Model Fs extremely rigid and taut feeling but this inflexibility can lead to cracking or snapping if subjected to considerable stress or shock - Model F122s are particularly known for sustaining such damage during shipping. By contrast, Model Ms typically have more flexible PVC casing that gives more room for damage absorption. Model F casing is also typically painted in a creamy colour, whereas Model M casing is typically dyed in their colour all the way through the plastic. Both Model F and Model M casing have notable textured finishes, but the use of paint for the Model F makes their texture and indeed entire colour more susceptible to wear.
The internal keyboard assembly is also subject to some differences. Model Fs have metal barrel plates and backplates, which are fixed together using metal tabs. With only two rare exceptions, Model Ms only have a metal backplate with a plastic barrel plate that's secured using melted plastic rivets. Whilst both keyboard designs are generally described as long-lived as evidenced by the fact a great number of even early to mid-1980s examples survive and function without issue today, the plastic rivets Model Ms can be an Achilles' heel of sorts as they can invariably break. When a significant number of them break in a localised area, the tension that holds the assembly together will diminish that will at first lead to a mushy key-feeling and eventually faulty registering. It's believed that handling, closeness to vibration and environmental conditions factor into how long they last. Model Fs can also have a weakness in the foam padding that lies between the barrel plate and capacitance-sensing PCB, which can invariably degrade in time. However, foam degradation typically doesn't result in a major technical fault with the typical side effect being that keys are more prone to rotating in their place. It only really becomes a significant issue if one opens up the assembly and allows the old foam to uncompress. Both issues can be permanently resolved by documented processes such as the bolt/screw mod or refoam mod respectively.
TLDR: Model Fs have more advantageous internal assemblies but Model Ms have more resilient casing. Whilst harder and tauter, Model F cases are unfortunately brittle and painted. Model M casing can flex a bit more and are dyed instead. Model Ms are subject to plastic rivet loss and Model Fs are subject to foam degradation, but a plastic rivet loss is a more serious issue for its host keyboard.
This will be considered mostly in terms of layout and protocols. Model Fs are technically closer to keyboard genesis than Model Ms, which means the first and most common Model Fs, the F/XT, missed out on key significant usability improvements made between 1981 and 1985. These included the solidification of the navigation layout by the DEC LK201 keyboard, the near-finished solidification of the ISO layout by various terminal Model Fs, and lock-lights introduced by the F/AT. The most common Model M, the Enhanced Keyboard, has all of these and can come with an ANSI or ISO layout that's basically the same as what most people use today. In fact, Model Ms are largely the reason we use these layouts today! The F122 has a more modern layout compared to the F/XT and the F/AT can be modded to a near modern layout, but both keyboards also cost more than an F/XT or a typical Model M and layout modding a F/AT requires additional time and effort.
Another score in the Model M's favour is protocol. Out of all the Model Fs, the F/AT is the only one that has a protocol and connector that is easily and cheaply converted for a modern PC (although of note, the Model F Labs reproductions are USB). The F/XT and all of the terminal variants require an active converter that is not stocked by major computer retail outlets or websites, requiring you to assemble your own or buy an expensive commercial option from orihalcon via eBay or tinkerboy.xyz. Most vintage Model Ms are AT and PS/2 compatible and most modern Unicomp Model Ms are USB compatible, allowing them to be easily used with modern PCs with at most a cheap active converter from Amazon for PS/2 Model Ms. And if you don't want to deal with any converter hassle with your AT or PS/2 Model M, Unicomp runs a service where they'll USB-convert your vintage Model M for you.
TLDR: Model Ms have the potential to be a less-fuss option compared to Model Fs, as they feature layouts you're more likely used to and a plug and protocol that are natively compatible with a modern PC or can be converted cheaply with commercial options.
In summary, you could say Model Fs are technically better but Model Ms are practically better. Most agree Model Fs feel better to use due to the properties of their switches and the sheer build quality of the keyboard itself. However, most also agree Model Ms are easier to live with. Especially if you're not familiar with keyboards from before the modern period, the most accessible Model Ms have layouts that are instantly recognisable without much need for self-adjustment. And should something go wrong with your keyboard, fixes for Model M-related problems are arguably more documented due to the popularity of the keyboard, and Unicomp exists to cover you with a repair service and most parts if something goes really wrong. Whilst they're familiar with Model Fs, Unicomp doesn't have much or any parts spare to help people with their Model F fixing or restoration projects.
Regardless of your choice though, if clicky, tactile and above-average heavy switches are your thing, you'll likely enjoy either keyboard. Hopefully, this page has summarised well the most significant differences and pros and cons of both keyboards. If you need any additional advice or clarification, feel free to get in contact with me or make a post on the /r/ModelM subreddit!