Hi. Moody96!
I'm not sure about all of the software that comes with those two controllers. In particular, I can't find a detailed description of the MPC Essentials software that comes with the Akai MPK mini mkII, so I don't know how it compares and contrasts with Ableton Live Lite.
I can tell you that Ableton Live Lite is fine for casual tinkering, but might be too "lite" if you're planning to do a lot of serious recording. Following is a comparison of some basic specs for the different versions of Live:
Live Lite:
- 8 audio/MIDI tracks [EDIT: That's 8 tracks total, such as 3 MIDI plus 5 audio, not 8 of each!]
- 2 send/return tracks
- 1 master track
- 8 scenes
- 2 audio inputs
- 2 audio outputs
Live Intro:
- 16 audio/MIDI tracks [EDIT: That's 16 total, not 16 of each.]
- 2 send/return tracks
- 1 master track
- 8 scenes
- 4 audio inputs
- 4 audio outputs
Live Standard and Live Suite:
- Unlimited audio/MIDI tracks
- 12 send/return tracks
- 1 master track
- Unlimited scenes
- 256 audio inputs
- 256 audio outputs
There are other differences, such as which virtual instruments and effects are included, but this should give you an idea of whether Live Lite would be adequate for recording purposes, or whether you'd eventually need to buy one of the other versions.
By the way, if money is an object (as it is for most of us), there are a few free DAWs you might check out, such as PreSonus Studio One Prime or Tracktion T5. Studio One is nice, but the Prime version doesn't support third-party plugins, and in general Studio One (as well as Ableton Live) doesn't support MIDI SysEx messages-- which you might not need, although if you do need them then you should be aware of that limitation ahead of time. On the other hand, Tracktion T5 does support both third-party plugins and SysEx messages. And I think GarageBand is free for the basic program, although to my knowledge it doesn't really support MIDI output-- MIDI input, yes, but not sending MIDI to external devices or exporting to MIDI files (if you need that).
As for the other software, the Alesis comes with Xpand!2, which has a variety of instrument sounds-- orchestral as well as electric-- whereas the Akai comes with a couple of soft synths, so you might be more inclined to one or the other depending on whether you're more interested in creating electronic music or music that employs traditional acoustic and electric instruments.
Of course, there are also free plugins available, ranging from soundfonts and sample players to soft synths. They might not be as polished or sophisticated as paid commercial programs, so sooner or later you'll probably want to spend some money on additional software instruments. But you should be able to find some free plugins-- as well as a free DAW, if necessary-- to get up and running regardless of which keyboard controller you decide to go with.