briank,
I've owned two Rhino 660s, and frequently went riding with a friend that had both a Rhino 660 and a Rhino 700.  Right now I own a Rzr XP 900, which admittedly is not the same Rzr you are considering.  I've owned 3 Grizzly 660s and 2 Grizzly 700s, and a bunch of other Yamaha's, all the way from dirt bikes to ATVs.  I've owned all of the other brands of ATVs as well, and I don't consider myself brand loyal, and really just try to tell it like it is.  Keeping in mind that my Rzr is not quite the same as the Rzr you are considering, maybe I can still give you a comparison between the Rhino and the Rzr.

I must say that I wasn't too impressed with the Rhino.  I had lots of problems with fuel delivery because of pieces of plastic crud in the gas tank from the factory.  This caused plugged fuel filters, plugged jets, and vapor lock issues.  I've never messed with a carburator so much to get a vehicle running correctly, but once dialed in it was at least fair.  My carburated Rhino 660s were faster and ran better than my friends fuel injected Rhino 700.  Reliability otherwise was quite poor as well, and my Rhino's left me stranded three times.  Build quality left a lot to be desired.  These things vibrate and rattle like crazy, and they're very loud to ride in.  Suspension quality is poor, stability is poor, handling is poor, all being compared to just about anything else (ATVs, motorcycles, Jeeps, etc).  Power is extremely poor, and this was the biggest complaint I had about the Rhino.  They were just incredibly gutless, and quite frankly boring to drive.

In comparison, the Rzr XP 900 is a major step up in quality.  Vibration, noise, and rattles are much much less.  Steering is easier.  Handling is night and day better.  Power is the biggest difference though.  A Rhino has something like 36 HP, and the Rzr XP has 88 HP.  That is a difference you can feel right now.  I shouldn't even have to mention how much better the suspension is, ... 7" travel vs 14" travel.  Serviceability is much easier, with easy access to spark plugs, dip sticks, and the air filter.

In the years since the introduction of the Rhino Yamaha has done nothing to really improve it.  Polaris has made improvements in build quality regularly.  At this point the latest Rzr side by side is so much better than the Rhino that it is hard to even describe the differences.  You ask if I like my Rzr?  The answer is a resounding yes.

[edit]  Just noticed my signature is from when I owned the Rhino.  Time to get that changed.  There is also one thing I like better on the Rhino than the Rzr.  I think the ultramatic transmission in the Yamaha is a better design.  The clutching on the Rzr is better for performance, but I like the Ultramatic transmissions design that keeps the belt from engaging and disengaging, ... it is always engaged.  That makes for a smoother start up and better engine braking.

I have a Warn 3.0 mounted on a Pro Armor race bumper.  It works well, and the 3.0 winch didn't break the bank as much as a 4.0 would have.

3TV

Now that is a very nice looking cage.  I wish I would have seen that before buying my two seater cage.  I also like the way it can be shipped in boxes, instead of on a pallet like a fully welded race cage.  It cost over $500 for just shipping with the cage I bought, and that was to ship it just one state away from where it was built. 

I liked that before and after post that badley started.  Maybe we should each do a before and after photo.  Here's my Rhino before and after:

Before

after

Now lets see your before and after photos.
3TV

You already answered your own question when you made that list.  And the first item on your list says Teryx.

Here are some pictures from the Logandale, Nevada ATV trail system.  Trails are very well suited for side x sides.  Plan on sunshine, with temps in the 60s this time of year.

3TV

For desert racing you will need a pit crew.  you can't expect to undo your harnesses and crawl out to fill it with gas each time you come into the pit.  And if you breakdown your crew is going to have to get your Rhino back out of the desert for you.  The sponsoring club will get the drivers back to the pits if they have to, but they are not obligated to tow your Rhino back.  At least thats the way it is around here.

Basic spare parts are a good idea, such as spare tires/wheels, fuel pump, fuel hose, fuel filter, air filter, spare CDI, spare belt for the transmission, and perhaps spare axle shafts.  If anything more complicated than that lets go you can pretty much count on a DNF.

Yes it is expensive.  I only make it to a few races each year.  Sponsors would help with some of the cost.  Right now I only get parts for dealer cost, which helps, but not enough.