Both can do recording, but the industry standard is actually Digidesign's Pro Tools. If you want the program that everyone uses, its pro tools. Walk in to any recording studio across the nation and probably 80% of them use pro tools.
Logic and Cubase are more designed for sequencing but they can do recording as well. Logic's recording leaves something to be desired. I don't know as much about Cubase's recording.
Another program you can look at is MOTU's Digital Performer. It's recording capabilities are better than Logic's and it also plugs into pro tools fairly easily. It also has excellent sequencing abilities.
All these programs have a fairly steep learning curve. Professionally, none of them are really "easy." Logic actually has a tendency to be easy on simple tasks, and really hard on more complicated tasks. I would recommend you buy a "learning Pro Tools/Logic/Cubase/DP/etc" book.
As for audio interfaces, make sure the interface you buy is compatible with the program you use. Pro tools is usually harder to find compatible interfaces but M-Audio makes a bunch of decent ones that run an "M-Powered" version of pro tools. I would suggest that if you want to start recording professionally.
If you want to get really crystal clear recordings, make sure you buy external pre-amps for your audio interface. Pre-amps built into audio interfaces are usually fairly cheap and don't have as clear of a sound as you would get with an external pre-amp.
Whatever your choice is, it depends more on how your recording sounds, more than the software you use. But just because the world is hooked on pro tools, is why I recommend that.
Lastly, I recommend you contact one of the professionals at
www.sweetwater.com. There is a bunch of really knowledgeable guys over there and I trust them a lot. They'll definetly be able to put you in the right direction