So, my thoughts on the subject.
In compactness, AE wins, period.
In power use, LP wins, as it doesn't require power except when you're actively moving items. This means that you can (ex) leave your system on in a partially chunkloaded area without issues. You can also access your items without power manually, which can be useful.
In convenience, LP wins. It is a lot easier and faster to use an ender chest + remote requester, and you don't need to worry about where you are to use it.
In flexibility, LP wins. Satellite pipes and provider pipes in particular are cumbersome and expensive to imitate with AE.
All in all? I'm trying an AE network now, but as soon as I get slightly more established I'm ripping it out and replacing it with a LP system. In particular the "access items and craft from anywhere" I cannot live without.