I've migrated a lot of network code from ACE to boost.asio at one point, and was very happy with the results for multiple reasons. I'd say you only ever need ACE if you're stuck with CORBA.
I don't know if Qt compares, did they add some async/reactor stuff?
I'll amend myself, you only need ACE if you're stuck with CORBA in the 1990's.
ACE was good 15 years ago, when C++ was immature, boost didn't exist, and OOP was the answer to all problems.
Boost is not a replacement for ACE. They're different libraries with different purposes, one is not an alternative for the other. Just because Boost wraps ASIO, doesn't make it a communications framework.