Chris, it's been a while since I cut any styrene, but I feel like I had an issue with the chopper and square cuts. Not square in the sense of looking down in plan, but rather if you looked at the cut piece from the side. I think there is deformation introduced from the pressure of the blade, or maybe it's simply the effect of the "kerf" at the beginning of the cut versus essentially none at the bottom of the cut? This seems to be more pronounced as the material depth increases.
And I also wish the blade could be brought straight down on the work, rather than pivoting, so that pressure is applied equally across the face. Years ago somebody made a chopper tool like that, I've seen it once or twice on the internet, but never in person.
EDIT: found them, the first is the Shay Wood Miter tool, and the second is called the Calibre Cutter. The Calibre is based on the earlier Shay model, apparently. They can be found via google search, or at this thread on the Atlas Rescue Forum. It's a thread about cutters, so it might be a good read anyway.
There are a couple of other issues with the chopper to be aware of. Not saying don't get one, just understand that they could be improved upon. If you buy one with the wooden (masonite, maybe?) beds, know that it will eventually get nicked up pretty badly at the point where the blade pops through the work being cut. I also found out the hard way that the threaded inserts used to screw the stops down can strip out if they are over-tightened. On the plus side, at least the original chopper has a long bed and fence.
The Chopper II is nice because it has a cutting mat insert, which can be easily replaced, or even just turned over or rotated. The other nice feature is that the fence is cast integrally with the bed, rather than attached to the top as on the wood bed models. The issue is that the thinnest materials can slide underneath the fence. I've had it happen with .005" stock. That can't happen with the Chopper II. Now, on the downside, the Chopper II bed is far too short in my opinion, especially when trying to use the stops for angled cuts or anything other than fairly short off-cuts. Nev has the right idea by mounting his cutter to a base that increases the bed length. It would be even better with a longer fence, say a metal straightedge glued or screwed in place.
Anyway, like Nev, I'd really rather saw heavier stock. I'd also really rather have a blade that rotated in plan to achieve miter cuts, rather than angling the stock away from the fence.
One thing to be aware of if you go for a mini chop saw like the Proxxon, is to check the position of the blade against the vise jaws, to avoid interference. Especially if you rotate the vise for mitered cuts. That obviously won't be an issue if you go with the mini table saw style instead.
If you want, I will go dig out my Chopper II, once I figure out where's it's currently hiding. I can cut some styrene and snap some photos to show the results.
Hope that helps,