My reply will be very biased, since I designed the Big Little Giant and I don't know much about the LiquidFoot. But I'm sure others will chime in to highlight the LF, the more info you get the better.
You can download the LG-X user manual to find out all details, I'll just add a comparison with the LF feature list posted by Voes:
> LF: You can choose between 6 PC or 12 PC. and every PC can be also a IA
> standard 16 IA's x 4pages. and with the new firmware pushing an IA more than 1s or 2s calls another IA!
LG-X : 250 banks of 13 switches. Each switch can be any type in each bank (preset, IA, momentary, trigger)
Standard : 13 presets per bank. "Extended bank" mode : 5 presets + (3x 8) presets in 3 sub-banks, single click access to each sub-bank through 2 dedicated select switches. (results for instance in 5 presets + 24 IA's per bank)
Optionally, a single switch can contain any number of presets, you can scroll through them sequentially.
> LF: each IA can send 20 ON and 20 OFF commands and that can be everything that's possible in MIDI:
LG-X : no maximum limit on number of commands per preset, only a limit on total amount of memory used. Any MIDI command plus a number of "Gordius specific" commands for special features. IA's have on/off message streams, presets or momentary switches can send messages on depress and on release.
> LF : Axe-fx tuner
LG-X : Only recently added. It's not yet documented in the manual.
> LF : Autoload of axe-fx presets (name and on/off settings IA)
LG-X : doesn't autoload Axe settings, and will probably not do it in the near future (LG-X is generally targeting multi-device control, with Axe settings being only a part of each preset setup)
> LF : Grouping of IA: if you have 3 IA's (for instance 3 delays) you can group them and if you push one, the other 2 will go in
> off-status
LG-X : same.
> LF : 4 expression pedal inputs. I rebuild my FV-500 with a toe-switch and now I can change my expression pedal
> from external1 (wah) to external8 (vol, pitch...) in my axe-fx
LG-X : 4 expr.pedal inputs. Customizable pedal transmission curve (linear, log, anti-log, user-drawn curves,...)
Possibility to create a "virtual toe-switch" and/or "virtual heel-switch" : preset can be selected when you reach the end of the pedal range, so any expr.pedal without physical switch can be used.
> LF : Cloning. great feature if you have a IA on another page. on page 1 you have drive and on page 2 also.
> if you change the state of drive on page 1 it will also change on page 2
LG-X : that's indeed standard behavior. IA state is stored independent from the switch(es) or bank(s) the IA is linked to.
> LF : You can trigger another IA
LG-X. (Not sure what that means) The LG-X setup introduces an extra level of "patches" vs "presets". Apparently confusing at the start, but in the end it enables you to combine several patch setups and pedal setups into one preset, or reuse preprogrammed patches in different presets. (mostly interesting when using it as a multi-device controller)
> LF : Sysex-commands: you can store and send more than 200 sysex-command lines
LG-X : Same as above : sysex is just one of the supported messages. Length only limited by total amount of memory.
> LF : And last but not least, great customerservice
LG-X : can't comment on that one... ;-)
> LF : In fact, I just can't imagine what the LF can't do
Just a few possible things I can think of - again, I'm sure others will be able to create a similar list of features that the LF has and the LG-X doesn't (it would be sad if both controllers would be a clone of each other...)
- graphical OLED display. Allows for a menu based setup on the unit itself. And for displaying set lists.
- USB connection. Allows for easy firmware/setup downloads. Also turns the LG-X into a standard MIDI-USB interface for connecting other MIDI stuff to your PC (Win,Mac,Linux)
- special footswitches. As reliable as Carling but more silent.
- compact. But you have to live with the strange switch layout. Many will prefer the classical grid layout which the LG-X doesn't have.
- accepts any cheap MIDI footcontroller as "slave". The slave (which sends PC or CC only) can trigger whatever complex LG-X preset.
- the rotary knob can be used as extra continuous MIDI controller for adjustment of any programmable parameter.
And some features which probably are irrelevant to many :
* use as metronome. Can send MIDI Clock with programmable BPM. Or show the BPM of incoming MIDI Clock on the display and LEDs. Plus taptempo functionality (change the metronome speed by tapping a switch)
* use as MIDI monitor (show list of incoming MIDI messages on the display)
* 2 MIDI IN/OUTs with programmable filter functionality.
* advanced programming options, like the use of data variables or MIDI channel variables... (see manual)
* use as keypad (enter a 3-digit PC number in order to directly select any of the 384 Axe presets)
* Gordius specific commands can be added to the message stream, for things like programmable delays, CC sweeps, loops, randomizing, etc.
But that's enough bragging in 1 message... sorry, I didn't intend this to become such a lengthy post.