I use both Mixbus 4 and Reaper on a PC, but also Samplitude for more demanding jobs. I also use Audacity for simple 2-track capture and topping/tailing.

Things I like about Mixbus 4 are its layout, signal flow, emulation of gain staging, operational convenience (knob per function) and, importantly, its sound. The stock compressors work acceptably well, but I don't like the stock EQs - they have the feel of being made to be limiting in operation and difficult to operate on a large screen, probably so that users purchase the add-on fully-graphic EQs at a cost more than double that of the whole package.

Things I like about Reaper are its lightness of demand on the CPU, ease of comping tracks and good graphical manipulation on the screen. The stock libraries are somewhat disappointing, particularly in the area of dynamics. Reaper takes a while to get used to - for me, it was not immediately intuitive to get beyond the first steps. There is a good on-line support community, although it feels a bit disconnected from the product.

Samplitude is in a different league (as it should be when you compare the price brackets), and I won't elaborate further on it here, other than saying that it constantly makes you realise what is missing from the lower-cost DAWs.

All these DAWs are interface-independent, so other than a quick compatibility and driver check before you finally settle on one, you don't need to factor that into your DAW choice.

I have no experience with Mixbus, but know a couple members here like it.

I've had good luck with reaper on all sorts of low power windows machines. I find it's metering good, and basic operation easy to jump into- editing, track creation/enabling, mixdown/rendering. Bussing and auxes maybe not so intuitive but I never even got that far. It's sound is clean, although not quite as much (clarity or headroom) as Samplitude or audition. It also does multichannel and high sample rates (11.1? 384k+). I find it's summing to be pretty good, not perfect, on par with digital performer and cubase ect, if not slightly better. (Summing based on subjective listening) it's also got some cool, imho, page based features for mastering making it easy to make mix tweaks, in the middle of a mastering session, by essentially "freezing" your mix session on a page sepearte from the mastering session, easily acessable by tab.

I find it's stock pluggins weak, and I dislike the menu based selection, which seems antiquated. Something I disliked in Audition as well. I found it's vsti stuff confusing and didn't bother with them. Not sure how well midi works with it either.

Overall it's my second or third daw of choice next to Samplitude, PT, audition, with audition being very clean sounding, having great effects, and spectral editing. Those don't run on Linux.

If your doing mainly audio work (not midi) and have some effects that are third party reaper is a solid choice. It is open source so it's editable on a code level if that's your thing. As someone who uses several different computers I like reapers fair licensing policy.

Mixbus is very interesting I just can't comment on it yet.

I just don't know enough about Linux to commemt on how well a certain platform will work on it.
There are some things I do like about MixBus; it definitely has an analog vibe to it that I don't believe Reaper has. I can't tell you the technical details as to why MB has a different sonic vibe than Reaper (or for that matter, Samplitude or PT) other than to wager a guess that it has something to do with the coding of the audio engine, and, that this was also intentional in an effort to make an emulation of a real Harrison 32 Series desk...
Although, I personally found V3 to be somewhat "clunky" in the GUI. I haven't yet tried V4.
And, Bos brought up a good point... if you want to purchase MixBus plugs, you'll pay more for one EQ than you will the entire platform. Add in other proprietary VST's such as compressors, verbs and delays, and you can end up paying substantial money for just the plugs alone.
I suppose the upside to doing that, is that you would have processing plugs that were designed specifically to work as a part of the MB platform; though I can't comment on the quality of these, as I never purchased any of their additional plugs.
I never had any issues using 64 bit Third Party plugs ( Slate, Waves, etc), but I can't comment on using older 32 bit VST's.
Your best bet is to do a fully functioning trials of both, put them through their paces based on how you work, and see what works best for you and what you do. It's all about productivity, and getting to know your DAW platform well is essential in order to achieve that productivity.
As far as the sonic differences between them, you have many options out there these days to achieve an "analog sound and vibe" on pretty much any DAW. And, actually tracking with tube or transformer-based gear (mics, pres, compressors, amps, etc) will also get you closer to that vibe as well.
FWIW :)
-d.

I'm probably not much help, but a few years ago I used Reaper on Windows and Ardour on Linux (MixBus is based on Ardour). I made some recordings with Ardour - nice and clean. I didn't care for some of the GUI or the menus, but that may have changed in recent years. I didn't like the stock EQ plugin at all. But Ardour always felt solid when using it and did a good job recording audio. I didn't care much for Reaper - it didn't seem very intuitive to me - but if it works as well on Linux as it does on Windows it would be great. Given the choice between Ardour and Reaper, I'd probably choose Reaper.