Always read the official Owners Manuals first
The wiki has been updated with information about Fractal Audio's new FM9 and FullRes IRs
Comparing the FM3 and FM9 and Axe-Fx III
Product Comparison Table
- The FM3 is the most portable all-in-one product with built-in foot switches.
- The FM9 is larger than the FM3 with more switches and more power.
- The flagship Axe-Fx III is a shallow 3U rack device. Controlling it by foot requires additional hardware (FC-6 and FC-12 foot controllers, or MIDI controller).
- Axe-Fx III: Auto-Switching front and rear instrument inputs with "Secret Sauce IV" Analog circuitry.
- FM9: one instrument input with "Secret Sauce IV" Analog circuitry.
- FM3: one instrument input with "Secret Sauce IV" Analog circuitry.
- The FM3 doesn't support variable (auto) input impedance, the Axe-Fx III and FM9 do.
- For best SNR, the FM3 provides four fixed stages of input level padding in Setup:I/O, while the Axe-Fx III and FM9 let you finetune the value.
- The Axe-Fx 3, FM3 and FM9 have a phones jack (some of the first FM3 units do NOT have this feature).
- FM3: Main out has balanced XLR jacks only.
- Axe-Fx III and FM9 have Main out both balanced XLR and 1/4" Humbuster outputs.
"FX III is 6 dB higher than FM3 on Output 1. 
- Axe-Fx III: three additional stereo I/O pairs, two designed for unity gain applications.
- FM3: one additional I/O stereo pair designed for unity gain applications.
- FM9: two additional I/O stereo pair, with one designed for unity gain applications.
- Axe-Fx III: SPDIF or AES (selectable) input and output.
- FM3: SPDIF output only.
- FM9: SPDIF input and output.
Pedals and Switches:
- The FM3 has two ports for pedals and (dual) switches.
- The FM9 has three ports for pedals and (single) switches.
- The user interface is the same.
- The layout grid is 12x4 on the FM3, and 14x6 on the Axe-Fx III and FM9.
- The Value wheel on the FM3 and FM9 do not have a built-in push switch, the one on the Axe-Fx III does.
- FM3: aside from modifications designed to optimize CPU on the FM3 (see below), the FM3 runs the same algorithms and therefore sounds the same when identical settings are used. Exceptions are possible, when later improvements and new features of the III can't be ported to the FM3 because of CPU constraints.
- FM9: runs the same algorithms as the Axe-Fx III and therefore sounds the same when identical settings are used. Some exceptions are possible, as documented in the wiki.
- The processing power of the III is the highest, allowing the most effects and functionality in presets.
- On the FM3, the delays share a core DSP with amp modeling. Reverbs have an impact on overall CPU usage.
- On the FM9, amp modeling, delays and reverbs each have their own dedicated core DSP. This enables ultra-high quality reverbs without a large impact on overall CPU usage.
Presets and scenes
- The number of presets, and scenes per preset, is the same (512) for the Axe-Fx III (original model), FM3 and FM9. The number of presets in the Mark II model of the Axe-Fx III is 1024.
- Presets for the III, FM3 and FM9 are semi-compatible:
- When importing presets from the III and FM9, FM3-Edit will try to convert the larger grid to the FM3’s smaller grid. Blocks on the far right columns or lower rows of the Axe-Fx III are put into the first available spaces on the left of the FM3 layout grid and are disconnected.
- Blocks which aren't supported by the FM3 or FM9 can't be imported.
- There can also be differences when the firmware on both devices doesn't exactly provide the same features and functionality, such as block types.
- FM3 has no Vocoder, no Tone Match, no IR Capture, no Real-Time Analyzer, no IR Player, no Crossover.
- FM9 has no Vocoder, no Tone Match, no IR Capture, no Real-Time Analyzer, no IR Player.
- There are less instances of certain blocks on the FM3 and FM9.
- Effect blocks on the FM3, FM9 and Axe-Fx III have the same number of Channels. Except for the Multiplexer (less channels on the FM3).
- The two Delay blocks on the FM3 do not have diffusion parameters.
- Reverb on the FM3 defaults to "Economy" quality mode.
- The FM3 and FM9 provides less looping time in the Looper block than the Axe-Fx III.
- The FM3 and FM9 may not have the most recent Pitch algorithm (at the time of writing) because of CPU constraints.
- The FM3 and FM9 do not support "dual source" modifiers.
- Maximum delay time is 16 sec for the Axe-Fx III and FM9, and 8 sec for the FM3.
- Reverbs require a lot of CPU on the FM3, much less on the FM9 (they have their own DSP core).
"The core modeling technologies are the same, but not all features are present on the lighter platform. For example, the FM3 doesn't have input dynamics or bias trem. At present, it doesn't have Master Bias Excursion. This is what I mean by different versions not necessarily in lockstep." 
- The Axe-Fx III supports Global Blocks.
- The FM3 and FM9 do not support Global Blocks.
- The FM3 has a single Amp block, where the Axe-Fx III and FM9 have two amp blocks per preset.
- The Axe-Fx III, FM3 and FM9 all support "Cygnus" amp modeling, with the same amp models.
- Some Amp block features are not available on the FM3, such as Bias Tremolo, Input Dynamics and Master Bias Excursion.
- Some Amp block features are not available on the FM9, such as Input Dynamics and Master Bias Excursion.
(comparing the FM3's amp modeling to the Axe-Fx III) "They are the same quality. Certain features were removed to allow the algorithms to run including the bias tremolo, input dynamics processing (...)." 
(FM3) "We removed all the superfluous stuff (bias tremolo, dynamic presence/depth, etc.) in order to get the core amp modeling to run on the slower processor." 
(FM3) "The Axe-Fx III contains various algorithms that allow you to enhance the amp modeling that don't exist on a real amp. I.e. dynamic presence/depth, input dynamic processing, etc. These were removed to allow the core amp modeling to run on the lower-powered processor." 
- The FM3 provides a single Cab block with two IRs, the FM9 has two Cab blocks with two IRs, and the Axe-Fx III has two Cab blocks with four IRs each.
- The FM3 and FM9 support the same factory cab models as the III.
- The FM3 and FM9 provide 1024 user cab slots (vs 2048 on the III).
- A limited number of Cab block features are not available on the FM3: Smoothing.
- FM3 and FM9 support Ultra-Res (added in later firmware releases).
- On the FM3, Cab modeling runs in a FIR accelerator. This FIR accelerator offloads processing from the CPU and, as such, doesn't reflect in CPU usage.
- FM3-Edit is the editor for the FM3.
- FM9-Edit is the editor for the FM9.
- Axe-Edit III is the editor for the Axe-Fx III.
- The FM3 has 3 onboard foot switches. The FM9 has 9 onboard foot switches. The III requires a FC controller (FASLINK II) or MIDI controller for foot control.
- The FM3 and FM9 provide Views for foot switch layouts (the Axe-Fx III does not, yet).
- The FM3, FM9 and III support FASLINK II.
- The Axe-Fx III can support up to four connected FC Controllers. The FM3 and FM9 support up to two.
USB and MIDI
- MIDI OUT and THRU are shared on the FM3 and FM9 (1 port vs separate ports on the III).
- The FM3 has a USB-A port, which is currently unused (the III and FM9 do not have a USB-A port).
- The FM3 provides 4x4 USB Audio (vs 8x8 on the Axe-Fx III and FM9).
- The FM3 is NOT a USB MIDI Device. It uses “COMM over USB” channels for Fractal-Bot and FM3-Edit, but will not appear as a MIDI device in a DAW or other MIDI program. The Axe-Fx III and FM9 support MIDI-over-USB.