All things being equal, having the 4L60E rebuilt (with beefier internals) is going to be much cheaper than converting to a 4L80E. The 4L80E is a heavier duty transmission than the 4L60E. However, the conversion requires a tailshaft speed sensor, plus new: output yoke (different spline setup), drive shaft, computer reprogramming, harness repinning, and ideally you'd replace the 10b axle with a 14b (next weak link in the drivetrain)
I've had my factory transmission rebuilt a few times since I've owned it. The last rebuild was done by a great local shop (I would NEVER recommend the shop that did the first two rebuilds...
). Regardless of who does your trans rebuild, I'd suggest going with beefier internals. There's a lot of room for improvement in the 4L60E when it comes to being in our trucks to say the least -they were designed for cars, not heavy trucks.
To your point about going through the entire trans, I'd highly recommend it if ANY component has failed (clutches, planetaries, TC, etc.). As
Martinjmpr stated, you're looking at the $2k+/- ballpark. The transmission internals aren't significantly different between the GMT400 (4L60E has 4 planetaries) and GMT800 (4L65E has 5 planetaries).
As an aside, It's a good idea to get to know your transmission folks. Even if you do the work yourself, they can be a valuable resource.