Peter,
At first you only need something that does the few basic things I discuss below and any of the DAWs should do that. Now Pro Tools is used by a ton of people, full featured, and its hard to go wrong with it. You never know what features of the DAW you may need over time. And really good MIDI editing functions are a must at some point, but likely not for you now. You also can't go wrong with the Logic Pro your friend uses (and it would be nice to just ask him questions he can easily answer for you if you have any road blocks).
But it really comes down to work flow. For example Cubase and Sonar have similar features, but for me Sonar is just a pain to use. Maybe because I started with Cubase. You may well just like the user feel of one versus another. Hard to say what will suit you best. But comfort is important and it would be good to try a few out somehow.
I think you can actually get a subscription to Pro Tools so you can try it out for a low cost on a monthly basis and if you like it you can either continue on the subscription or buy it. That might be a good way to go. If you don't like it you can cancel and try another one. Logic Pro looks like its only a couple hundred bucks (Logic Studio includes that I think and is the flagship product). MOTU Digital Performer is also a great MAC based tool (but more expensive and more than you may need). I don't have that much experience with Garage Band, Reaper or Fruity Loops (now FL Studio) but many use them - and people really love and rave about Ableton Live. But in the end, Garage Band is so cheap (almost free compared to the others), frankly it may be a good starting option to get your feet wet. Many say that it's easy to move from Garage Band to Logic. (I've only used Cubase, Sonar and Digital Performer and some I have not mentioned here so I don't want to steer you wrong).
So I would investigate these below and maybe for a few bucks just get Garage Band to get your feet wet. Who knows you may not need anything more for a while. Omnisphere lists it as one of the major tools they work with. (KISS is our mantra in the computer world).
Garage Band, Logic, Pro Tools and Ableton Live.
The high end tools also are now meant to do scoring to video as well having SMPTE interfaces, etc - this may be of interest to you down the road.
Some assumptions and info that may be of use to you:
Unless you are in the true digital music production business you are likely only going to use a small fraction of the features of almost any of the major DAWs. Which is good because you only want to learn the few things you need to to best apply this to your music. I would think initially what you will want to do is load up a library in the DAW and play it in Monitor mode - that is, not record it in the DAW but spew it back to your speakers & Roland recorder so basically you are treating the DAW as a means of playing the Haken or your MIDI keyboard in a way you have always done. You are just basically routing it through your DAW and computer that will function as a new instrument (or in this case 10,000 of them with Omnisphere 2). From there you can worry about actually recording on the DAW and all the things that go with that, including recording MIDI, not audio, and then manipulating MIDI in various ways playing that back through the plug-ins. But a lot of Omnisphere manipulation is going to be very easy using its configuration tabs - setting reverb, stereo width, and other parameters you control through the Omnisphere screens (that you guessed it can be accessed through your DAW).
So you really are (I think) interested initially in:
1. Connecting the MIDI instruments/controllers to the DAW/Computer through your MIDI interface
2. Bringing up the DAW, creating some instrument channels that map to MIDI channels and loading your plug-in sound library patches (possibly Omnisphere2 in this case) into those channels which it is assumed you are playing from the Korg or Haken (you can load in a mode that will set individual MIDI channels or you can load in an omni mode that will appy all MIDI channels to the instrument track you assign - so for example all the fingers you press on the Haken come out using the same sound). For example, if you assign an instrument track you create to MIDI channel 1 and you play a chord on the Haken and the Haken is sending each of the three fingers pressed on a different MIDI channel (only first note assigned to channel 1 will be played - unless you are set to Omni/Poly Midi mode). [That's an important tip you need to know for the Haken. But the piano will default that everything you play goes to a single MIDI channel - but make sure the MIDI channel the Korg is set to play on matches the MIDI channel you assign to the instrument track you create in the DAW].
3. Set the DAW so that when you play, sound comes out your sound interface to speakers or possibly routed to your recorder without having to record. This is normally setting to the "monitor" mode that all DAWs will support. This will let you play the thing like its an instrument and hopefully there will be no delay to worry about.
Hope this helps.
Rich