As 10.6.8 is supported on both Mac Pros the simple answer is yes, you can transfer your disks over to the newer Mac Pro and your installation will work as it did before.
Assuming you don't do something silly like accept the free update to Yosemite (which is supported on the Mac Pro 3,1) you will be able to move the disk back to the older machine if you need to. As long as you stay with 10.6.8 there are no updates that will break the ability for your 10.6.8 startup disk to boot the older Mac.
Having said that, if the newer Mac Pro is of a reasonably higher spec - and you want newer server features such as Profile Manager - you may want to think about performing a clean installation of 10.10 (as well as purchasing the latest iteration of OS X Server), then migrating the data over from the older machine. The only cost is the purchase of OS X server, and that's not exactly going to break the bank.