Hi!
Oh yes, you definitely want to fly the Cessna T-37, the best trainer ever built!
It's a classic. A classic is something that used to be good or popular, but has now been bypassed by current technology.
So, the T-37 may have a few quirks of a typical classic, for example:
The air conditioning doesn't work on the ground. It doesn't work in the air, either.
It is slightly noisier than the T-6. For example, you wear a pair of foam plugs under your noise-attenuating helmet, and you still have hearing loss after UPT.
When you push the throttles up to takeoff, nothing happens, except your ears recoil in pain, and it's hard to hear the tower telling you that they only cleared you for an IMMEDIATE takeoff, and asking you why you're still on the ground. Then, after about 10 seconds, you check to make sure the throttles are at their stops, because, still, nothing seems to be happening. Then, you look over on the parallel runway and watch the C-172 accelerate away from you down the runway, rocket into the sky, and dissapear into the wild blue yonder.
In return for the massive lack of thrust from both of the T-37's mighty engines, you still get crappy range/duration.
There is no pressurization, so those cross-country flights at FL 250 (it takes about 1.5 to make it that high) are a real pain in the a$$, not to mention about everywhere else.
The T-37 is an excellent beginner instrument platform. That is because the gauges and instruments have been randomly scattered around the aircraft. Since there's no good way to scan the instruments, you can do it however you want and the instructor can't tell you you're wrong. (A civilian guy I was flying with, in a real jet, went with me and looked inside a T-37 cockpit. He said, "Oh my g0d!!!"
The "ejection seat" is supposed to work correctly, as long as you're withing parameters: At least 10,000' AGL, with a positive vector away from the ground, you're flying fairly wings level, and you're going at least 450 kts. (An instructor and student I know ejected out of a burning T-37 in the pattern. Just after takeoff, it caught fire. The IP instructed the student to eject first, and then the IP ejected. I told him it was very noble that he looked after his student and put his safety first. The IP told me he thought they were too slow and too close to the ground when the student got out, and he wanted better parameters!)
But, best of all, is the sexy, sleek lines of the T-37! It just screams to all the ladies, "Date me, because I'm a JET PILOT!"
So, you definitely want the T-37, it's head and shoulders above the T-6
Cliff
YIP
PS-I hope you get the T-6! The main thing to do is take your time with the engine controls. Positively identify which control you have in your hand. You don't want to shut the engine down by mistake, especially close to the ground unless you want to test the excellent ejection seats.
Real men fly the Tweeter. 
