If you are recording vocals and like a vocal harmonizer, PAx4 has TC helicon vocal harmonizer. Kronos does not.
If you are looking for ready made rhythms with several quick fit fills, breaks and intros per each rythm, then PAx4 has all that plus added parts like bass that follow along with the rythm and notes played. Kronos does not have that even though Karma comes close.
Kronos does have Karma which goes a long way with accompaniment but it is hard to dial in the *traditional* style fills and intros with karma GE. You can get some fashion of fills and breaks and intros to work for you from Karma but it will be a noticeable difference from what and how PAx4 does.
Kronos rythms have fills built into them and kronos has a potent rythm making&arranging feature in Sequencer mode (pattern RPPR) and that can couple with Karma's extensive rythm design features. All that can be put into midi tracks, chopped and re-fitted, one rythm layered with others to make one hybrid and other tricks.
So... When it comes to what you can do from scratch, wether it be making rythms, designing sounds, redesignng existing sounds, sampling wizardry, extensive high quality sounds across various synth engines with open door to bring in third party sounds and remove factory sounds you do not want, linking to and working with external devices, playing huge layerd sounds with rythm and arpeggio, huge internal memory, output and input plug holes and assignability of their function and routing, internal routing of everything from effects to controls and on and on, Kronos has a bit of an edge over the rest.
Huge internal memory and storage also. Kronos.
If you can do without the PSR series method of rhythm accompaniment using ready made bass and drum parts with fills and intros easily tapped in on cue, then you will enter a whole new world that makes PSR series look like a toy(although the latest versions of PSR are right up there with PAx4).
If you need the PSR style of easy ready made rhythm/accompaniment, then go with PAx4. You will also have fun with TC helicon vocal harmonizer.
You will miss out on Karma and that is a lot.
Kronos synth engine sounds are better than PAx4 from what i listened to on youtube.
I am one who needs PAx and PSR style accompaniment with ready made fills that can be called up from varieties ,on cue with just a touch. I still got Kronos instead and planned to get a hardware drum machine for an extra $500. Skipped TC helicon and get Karma instead. I don't sing anyway.
Also computer software synths and DAW with Kronos is what will outdo anything i can think of. You can get computer based vocal harmonizer plugin, Karma has a software version that opens up an alreay vast Kronos Karma suite into a bigger and more customizable suite of GE's.
Kronos- better sound with karma to add but no TC helicon or traditional style drum accompaniment.
Possible work arounds with software though.
http://www.korgforums.com/forum/phpBB2/ ... 48bd3051d6
PAx4-lesser sound quality and has TC helicon voice harmonizer but no Karma. It has an extensive traditional style rythm accompaniment similar to PSR accompaniment but much more extensive in more ways than just rhythm styles. Newest PSR series have almost caught up with PA-x4 by closing in on Tyros-5 capabilities.
You will miss a lot without Karma but maybe it will be ok because you won't know what you are missing and PAx4 has more than enough for advanced music making.
Not sure which system is harder to learn, but both are very similar navigation layout. Korg modern style of workflow.
Karma is one section that makes kronos harder to fully learn.
I went with Kronos for the sound quality and 88 key graded hammer action. I rather keep my fingers trained on heavy keys and quality feel. I feel i am missing out on PAx4 offerings but i can easily make up for that and beyond with my Dr.880 drum machine and a computer based suite of all kinds of stuff that offer more than any of the major synth makers' flagship equipment.
Get the keybed right no matter what you get. Get the key feel and function that is right for your needs. All else can be substituted with external devices and computer based plugins over time.
hi friends, 
, then start with Kronos. The things Kronos can teach you over 5 years will make PAx4 easy if you decide you want to move to an arranger to make things simple and quick. 
