The T-6 is far, far, far...the way to go. I fly it in the reserves and have had only a hand full of right ups(mostly radio stuff, i.e. xc talk problems between the front and back).
It has been online for five years now and has had two engine failures, and a couple of gear problems but other than that I cannot think of any other major problems. I think it has a good safety record and the only crash was a no brainer PE.
The T-37 is a good bird but just plane old. Old avionics, old ejection seat, old airframe, old engines(it has two of em what a crazy concept for a primary trainer. I never would want a stud out in the area solo and lose a his one and only engine. Oh wait the T-6 only has one eng......)
But seriously the T-6 is a great aircraft that will do just about anything and the AD IPs work really hard with the studs(harder than I would) to get them through. The plane will not last as long as the 37, but it is not intended too.
If you have the choice don't let anybody talk you into the old be one of the last to fly the tweet guys. You will regreat it in hindsight.