Converter adaptor <should> still work. Personally, I like the adjustability of the shift point with a E trans. If you are running close to a stock PCM cal, there will be some benefits of running the E with the stock controller. If you plan on towing and hauling with your truck, the stock cal has all kinds of trans protects in there to keep temps down (locking TCC in 3rd and 4th under heavy loads) as well as the ability to set it up with a factory tow/haul switch.. To go one further, the LSx specific transmissions accomodate a slightly larger converter, and they are significantly more efficient than the older ones (about 1/2 mpg back-back).
No worries about getting the TV cable right.
It's just kinda nicer. Depends on how nice you want to make it.
My 93 had a 4L60E in it already, but when I did the 4.8 swap (possibly soon to be an Aluminum 5.3

) I bought a 99 LS1 trans to go with it. No adapters, better factory converters, drives like a 2002 Sierra would.
If you are putting an aftermarket converter in, then some of this may not even matter to you. I wanted more power in my truck, but I wanted it to dfive like factory, and be able to tow with confidence.