To know which transmission was used, look on the inside of the glove compartment door. There you'll find the RPO Codes printed on a white sticker. You'll see as such:
- M30 - 4L65e (Transmission, 4-speed automatic)
- MN8 - 4L85e (Transmission, 4-speed automatic, heavy-duty)
More than likely, the Avalanche has the 4L65e in it, unless the Avalanche was a 3/4T.
While you can put the 6L80/6L85/6L90 in place of either of the other two transmissions, it's not an easy chore. There are lots of things to consider. To do it the easiest, get the entire package out of a donor vehicle ... engine/transmission/xfer case, along with all the wiring and electronics. This will ensure everything will work right when you bolt it up. This is probably the easiest way to get it done, but will cost you a bit more due to having to get the entire package (you could sell everything out of the Avalanche to recoup some of the cost).
Interchangeability between the full line of Chevrolet/GMC trucks/vans should give you the ability to find the combo you'd want. If you decide to go the full swap route, look beyond the Avalanche for what you need. I'd highly suggest finding a 6.2L engine with tranny/xfer to compliment if you're going that route.
I believe there are stand alone controllers for these, but you'd have to research it.
The overall length of the transmission is different between the 4L's and the 6L's, so you'll need to have a new cross member made as well as having the drive shaft lengths corrected and rebalanced.
The transmission should bolt up directly to the 6.0L engine. The bell housing between all of the different types bolts directly to the LSx engines without issue. I'm unsure, but believe there may be a different flexplate used between the different types of transmissions (I'm not 100% positive on this, though). If so, more than likely there are different torque converters used as well.
Either way you do it, the cost is going to be pretty extensive to accomplish. If the reason you are considering this is better fuel mileage, the word on the street is this is pretty minimal mileage increase and really isn't worth it in the long run considering the cost and work you have to put into it to accomplish the task. Where this swap really shines is the difference you'll see while towing with the vehicle, as fuel mileage will go up in this case. If you are just looking for a stronger transmission, I'd highly suggest you have your transmission rebuilt by a tranny shop with premium performance parts which should provide better overall torque capacity.