I had an '00 Silverado Z71 Ext Cab 4x4 with the 5.3L. For a general all round truck it was great. But when it came to towing anything other than in town it sucked. I upgraded to an '07 NBS Silverado Max LT2 4x4 with a Trifecta tune and I love it. I probably wont ever go back to the 5.3. One thing I don't like about the 6.0L is the fuel economy. It sucks, but I like the power the 6.0 has. I bought my truck from Dave Smith Motors in Kellogg Idaho. I got a deal that no one here could touch, plus it gave me a reason to head back home to Montana.
If fuel economy isn't a deal breaker for you than the 6.0 is the way to go. The 5.3 is ok, but by the time you come all the way down from Alaska, through the maple leaf, into Washington State, across into Idaho (don't forget the potatos) and into Montana...that's a lot of towing on a tired 5.3. That's a lot of towing even for a new one. I would recommend the 6.0. You'll find that you'll have less trouble with the tranny, rear end, and engine if you do. Take it from a guy who's gone through it all with the 5.3.
By the way, besides the above mentioned trucks I've owned and currently have I also have an '05 GMC 2500HD SLT Duramax and Ali tran for pulling my 5th wheel. For towing the Duramax and Ali is no competition. I also have an '05 GMC Sierra 1500 SLT Z71 4x4 with the 5.3 that I don't use since I got the '07 Max.