It's a common myth that Reason doesn't allow for live recordings, it does, but there's no plug in and play option. Most (if not all) DJ's record their sets so have some way of recording live instruments. With Recycle too (I don't see much point with having one without the other) you can manipulate the live recording, splitting it up, resampling, changing pitch or tempo without affecting the other etc and then save it as a .Rexx file that compresses without sound quality loss.
The main drawback with Reason is the lack of VST's, however there is a way around this also. With a free sequencing programme open the VST you want to use in Reason, save the sounds, one after each other in the same track, then export to Recycle, now splice up each sound (up to 127 in total), then load it in to Dr Rexx in Reason. I know this is still a little limited, like for example the velocity is pretty much set when you first sample the sound, but that's the same with any sampling and if you really want a bassline using that VTS, in Reason, then it's good enough.
One massive plus with Reason that you don't get elsewhere is the ability to see the ahrdward and wiring, for me anyway this made things so muc easier than looking in menus and drop down boxes. Most of us are DJs after all, we're at home with connecting leads and such. I would have never learnt things like side chain compression as quickly without Reason.
Personally at the mo I use Reason, once I've built my PC I will be using Reason rewired with Cubase 4. I've also used Logic and Protools. I wouldn't say Reason and Logic are fair comparisons, it would be better to compare Cubase to Logic and in all fairness there's very little to pick between the too, it'll probably depend more on your OS. If I were starting out again, I'd get Reason and Recycle (again) learning things the hard/long way is sometimes better if you stick at it. If you're really dead against Reason and running WIndows, then Cubase, maybe one of the light versions, like LE. In fact Lexicon (Audio Input manufacturer, among other things) give away Cubase LE with even their more basic models. Seeing as you may need an Aduio nput device this could be the way to go. Saying this Behringer also used to give away a basic copy of Appleton with their midi keyboards too.