The Avalanche is on the same chassis as a Suburban and the Tahoe is on a shorter chassis. The Avalanche will have limited payload. I don't think there's enough payload on either truck for an 8k trailer. I think the payload will be around 1,300#, depending on trim level. I have a newer Avy and payload is my limiting factor. My thought is that the Avy will be very stretched even at 6k. The Avy is a heavy truck and a bit on the sluggish side compared to the new trucks. The Tahoe is probably lighter and snappier, but the shorter wheelbase may be a factor to consider if the trailer is on the longer side. Both trucks seem to fetch a premium price in the market relative to similarly equipped/type vehicles.
If you are a GM fan, I would suggest a similar year CC Silverado with max tow package.