I use the 24-120 more than anything else, it's as close to a replacement for my DX 18-200 (now sold although I keep regretting it) that I have at the moment.
Your next question is probably how good is it. Well, I'm very impressed. I tried it against a 24-70 2.8 the other day. Pixel peeping the 24-70 resolved more detail on my test (not massively), but it has less range and no VR.
I chose the 24-120 over the 24-70 when I went FX and it wasn't the cost that swung it. So far I'm pleased with the results and my decision. I'm probably going to get the 28-300 at some point as a true travel lens, even though I surprise myself that I don't miss the range that often.
Depending on your requirements the 24-70 may be the better choice, but not for my current use.
I went through a similar thought process between the 14-24 and the 16-35. I chose the latter because it better fitted my needs including taking filters and it's also a very sharp lens.