They both get basically the same tranny, with a few differences. It is a 4T65-E, which means 4 gears, transverse mounted (not front to back like a Camaro), 65 means it can withstand 650N-m of torque (I think). Not sure what the E means, probably Electronically controlled or something like that.

Here is where they differ. The L36 and L67 have different transmission RPO's. The difference between them is the torque converter diameter and the "beefiness" of the gearbox.

So it is much more likely that you will kill your tranny by adding onto the L36 than having a stock L67.