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Here's a quick comparison chart of some looping devices avaiable today. It doesn't cover the the market completely and I have on purpose selected a few functions that I think make sense for comparing the devices. Please feel free to contact me with suggestions on how to improve this chart. If you see the sign * inside a cell it means the issue is better explained down at the Enlightening Comments at the bottom of this page. Share on Facebook

  Overdub Feedback Undo Multiply Quantize Reverse loop MIDI Presets Sync Cut n Paste slices Pitch transposing Time stretching Tap tempo Max numbers of loops multiple loops in parallel Audio channels, Tracks Stereo recording Built-in storage option can run on battery Memory RAM
Echoplex LoopIV yes yes yes backwards scalling off layers yes yes yes yes yes MIDI clock, Brother, pulse yes half speed no yes, two taps defining initial loop cycle length as tempo base 16 no 1 mono no no, externally via MIDI no 16 MB
Repeater yes yes, but only in Overdub Mode yes, deleting only the last layer. When still in Rec Mode all new layers are deleted. yes sort of... yes yes no MIDI clock, beat, tap no MIDI notes, MIDI cc, manually yes yes 99

no
one loop may have four tracks

 4 mono or 2 stereo yes, by linking two mono tracks CFC card no 8 MB
Boomerang 2.0 yes 7 fixed levels no no no yes no no no no

half speed. Interval can be changed from an octave to a lower 2nd., 4th., 5th, or 7th.

 no yes, sort of... In version 2.0 you indicate the loop length and the device extrapolates the tempo 2 no no no no    
Line6 DL4 Modelling Delay yes no no no no yes no yes no no half speed no no 1 no no   no yes  
Boss RC-20XL yes no Yes. Last layer has Undo + Redo no yes related to tap tempo yes no yes no no no yes, but not fluently while loops are running yes 11 no 1   16 min mono yes battery or AC  
Looperlative yes yes no yes yes yes yes ? MIDI Clock, internally by first recorded set as master track no half speed no ? Many! Only limited by 128 MB RAM yes. synchronous, poly-rhythmic or non-rythmic loops is possible 8 stereo yes no no 128 MB
Digitech JamMan yes no yes no no no no no no no no no yes 99 no 1 mono no CF-Card; PC via USB   128M-2G CFC
Zoom G2 yes yes no no no no yes yes no no no no yes 1 no no no no yes  
Electro-Harmonix 2880 yes yes no no yes, for 1 bar length yes, action taken on all five tracks yes no yes, MIDI clock no half speed, octave button affecting all five tracks. Tempo slider also affects pitch. no, pitch changes with the tempo no 1, but with 4 tracks. Mixdown to 5th track can free up the 4 tracks for more looping no (?)
one loop may have four tracks		 4, can be mixed down to a 5th stereo track yes, by linking two mono tracks Flash card, 128 MB to 2 GB, USB computor backup and restore no  
Roland RC-50 yes no
(can be achieved if you bridge SubOuts with AuxIns)

yes

only one layer back - then "REDO" back again

 no
(can be achieved if you bridge SubOuts with AuxIns)		 yes yes yes yes
(even audio for old loops can be saved in a patch)		 yes no yes
(but it sounds horrible - unusable IMHO)		 yes
(but it sounds horrible - unsuable IMHO)		 yes
 3
(but then only one playing at a time)		 3
(but then no "Next Loop")		 3 yes 49 minutes in mono (half of that in stereo).
99 patch presets.
USB to /fromcomputer. Good editing/library software bundled.		 no  
Boss RC-2 yes no yes yes yes no no no no no no yes, but not fluently while loops are running yes 11 no 1   16 min mono

yes
battery or AC

  
Electro-Harmonix Stereo Memory Man with Hazari yes

"yes"
only during overdub

 no no no no no yes no no varispeed (continuous half to double speed) yes
(via tap tempo)		 yes 1 0 2 yes no no -

Boss DD

-20

Yes, kind of:
sound-on-sound-recording
in SOS mode		 yes no Yes, kind of: only in Delay Mode no reverse delay setting no 4
(flash RAM)		 no no no no yes 2 'yes* 2 yes no yes
battery or AC		 holds 23 seconds of audio
  Overdub Feedback Undo Multiply Quantize Reverse loop MIDI Presets Sync Cut n Paste slices Pitch transposing Time stretching Tap tempo Max numbers of loops, linear multiple loops in parallel Audio channels, Tracks Stereo recording Built-in storage option can run on battery Memory RAM
Logelloop
OS X		 yes both traditionally summing layers OR each new layer given its own channel in the loop yes yes (but no "redo") yes yes (for mixer and effect preset changes) yes yes yes swapping between mixer and effect presets as musical performance no no yes yes yes 3 as default but many more linear loops can be created and lined up yes, but rather l10 layers of the same loop. Layers can have different length though 10 loop layer channels, 2 VST plug-in channels and 1 chanel for built-in effects yes yes. can save files and has a syncable "file player" aside the looper yes, if laptop battery  
Ableton Live OSX/XP no no* no* no* yes yes* yes yes yes yes* yes* yes yes Many! Depending on computer spec's yes   yes yes yes, if laptop battery  
Lexicon PSP42 OSX/XP yes yes yes no no no yes yes by the host appl   no half speed no yes       yes no yes, if laptop battery  
Augustus Loop OSX yes yes no yes* sort of yes yes yes by the host appl yes no MIDI notes, MICI cc no yes 1 per instance     yes no yes, if laptop battery  
Sooper Looper Linux, OSX yes yes yes yes yes yes yes yes by the host appl yes no half speed, rate shift no yes Many! Depending on computer spec's     yes no yes, if laptop battery  
AU Looper OSX yes* yes* yes* yes* yes* yes* yes* yes by the host appl yes* no yes* yes* yes* 4 per instance yes   yes   yes, if laptop battery  
Mobius, XP yes yes yes backwards scalling off layers. Customizable yes yes yes yes yes MIDI Clock, internally by first recorded set as master track yes yes (not perfected yet), half speed, rate shift, yes (not perfected yet) yes Many! Depending on computer spec's yes. synchronous, poly-rhythmic or non-rythmic loops is possible 8 stereoper instance, or more if you tinker with the code yes yes, store loops or record complete performance to the computors drive yes, if laptop battery  
Loopy Lama XP, OSX yes   yes     yes yes   yes       yes           yes, if laptop battery  
Radial
Mac OS		 yes   no       yes   yes yes yes no             yes, if laptop battery  
  Overdub Feedback Undo Multiply Quantize Reverse loop MIDI Presets Sync Cut n Paste slices Pitch transposing Time stretching Tap tempo Max numbers of loops multiple loops in parallel Audio channels, Tracks Stereo recording Built-in storage option can run on battery Memory RAM


Relateded links you may find useful:

Enlightening comments:
Augustus Loop Multiply: (Os)
If you turn off the 'tape inertia' feature, then you can change the loop length to anything you like, while you're looping, with no glitches. So you can record a phrase and later change the loop time to e.g. four times the original length - which is effectively a multiply. The joy of the complete flexibility this gives you is that you could e.g. record an 8 beat phrase and then change the delay time to 11 beats. So you have fractional multiplies going on, if you so desire. Same applies in reverse - you can change the loop time to lower than the original time. So e.g. go from 4/4 to 3/4 seamlessly if you like.

BOSS DD-20 multiple loops in parallel: (Rainer Thelonius Balthasar Strschill)
I describe the "parallel loop" function of the DD20 in some more detail below, but the quick answer is still "yes" (2) (Some of the details here do not apply if one of the modes in question is the stupid "SOS" mode): The DD20 has four memory slots to store your favourite settings and then switch between them and "manual mode" (i.e. what you set up with the dials and knobs). It also has a "seamless switching" function which will have the last delay playing - only disconnected from the input as well as from the controls - if you switch to a new memory slot. This last delay will then continue playing either until it has faded out or until you switch memory slot again. Note that you lose control over that "last loop" completely, so you can't adjust feedback or volume or even go back to it and overdub further. But it sure does qualify for your description of "making changes to one loop whil still hearing the other looping on". As a matter of fact, you can even create four loops in parallel, namely if you choose the double delay for both your memory slots ;)