The difference between the transmissions is the governor. The RH is mechanical and the RE is electrical. The drive shaft is probably shorter on the RE because the transmission tail shaft is shorter. No mechanical governor in the tailshaft housing for the RE. I don't know if the mounts are different or not. They look the same, but I have not done any measurements. The 4X4 shift rod may be a different length. The front drive shaft may be longer.
If you manage to get the RE mounted then you have a problem with the electrical hook up. The RH has a three wire connector. The RE has 10. The RE requires a PCM that is different than the one for the RH so you will need one of those from a '96. I have no idea what sort of difficulties you would run into trying to adapt a '96 PCM to your truck.