Not the best to answer, but I have heard the CSP2+ several times and the S7 only once through a system I wasn't familiar with. I think these amps will be on par. When I heard the S7, the system as a whole was worse than any setup I heard the CSP2+ with, but I'm giving the S7 the benefit of the doubt due to the credibility of the crew here.

I'm assuming the CSP3 is very close to the CSP2+. The CSP2+ may not have been developed for the HD800, but it is a very well regarded match on HF. Nick Dangerous, whom I visit 3-4 times a year, owns this combo with a Resonessence Concero, and when I compared the BHA-1 and CSP2+ (w/Concero), side by side, I found only slight differences. The BHA-1 combo was a little brighter and more energetic on the whole, but the CSP2+ combo was not warm, just neutral and clean. It had a liquid sound to it, in that it was smooth, but not dulled as many 'smooth' setups tend to be. Nick has rolled lots of tubes in the amp and found a match he likes and I have to agree that he has dialed it in nicely. I have repeatedly recommended it as the only amp at $1000 (no longer in production, unfortunately) I thought was worth spending more than a Matrix M-Stage ($280). At $1250 the CSP3 is not quite the automatic recommend, as it's getting into contested territory.

I really detest the styling of the CSP2+, but that's just me. I did prefer the BHA-1 slightly, but I could have been happy with a CSP2+, as long as I was provided a blindfold. The CSP3, fortunately, is marginally better in this respect.

If you are shopping for an HD800 amp, I would put your plans on hold for a month. There are a couple amps that have potential to be great with the HD800, among other headphones, that will be shipping in a couple weeks, and they are in this price range. I will be comparing the GS-X mk2 and these amps, and I'm sure others will have their views.

edit -

Did some looking and indeed the CSP3 should be very similar sounding. Here is the blurb from Decware's revision history:

CSP3 / Manufactured from 2013 to present.

This version features the same great circuit in a completely new more ergonomic and better sounding layout.  A high mass powder coated steel plate with black textured finish adds several pounds and the improved layout makes it possible to offer the larger sized cryo treated beeswax caps.  Sonically this unit has improved transparency and blacker backgrounds - two things that didn't need improving but simply happened as a result of the new layout.

Just to throw a wrench in the works here.  We have a local guy with a lightly DIY modded csp2+ (I forget what he did) and in my listening time with it it's one of the best hd800 setups I've heard yet.  I do have had a bit of experience with the hd800 and various amps including the s7.

The s7 is probably better for a variety of different phones IE more versatile of an amp, but I have not done extensive listening with the csp2+ with other headphones to know for certain.

Not the best to answer, but I have heard the CSP2+ several times and the S7 only once through a system I wasn't familiar with. I think these amps will be on par. When I heard the S7, the system as a whole was worse than any setup I heard the CSP2+ with, but I'm giving the S7 the benefit of the doubt due to the credibility of the crew here.

This comment kind of confuses me since it was my s7 I think you are referring to.  If I recall correctly, you moved your dac to the s7 to listen to it.  Admittedly, the source when it was on the DA11, or on your dac was USB since it was a portable source, which sucks.  The da11 sounds noticeably thin out of USB in my opinion.

It also had the stock tung sol tubes at the time, which also aren't the best match.  I need to make it out to the next dallas meet with my new setup and hopefully a portable source that isn't usb.  At the meet you heard it, I had barely had it for 3 days, it really wasn't done justice at that point.

All that said, to add to the topic, I think the CSP2 is outstanding for the price, and when comparing retail prices I don't know that I'd recommend the s7 over it.  The CSP2 is a better value as far as I'm concerned, and I say that as a S7 owner. 

Just a couple things if you get the CSP3. 

1-make sure at least one of the jacks is 4-pin XLR.  You'll want that, trust me.
2-Do NOT get the Beeswax cap upgrade, that's what Audezes are for.
3-If you listen to alot of fast music like speed metal, the S7 might make more sense.  I doubt the 5AR4 rectifier would be as fast sounding as the S7, though some might notice a difference.