If you like multiplayer, and shooters, quite a bit grab BF3. It's a great game to play online. Although I would highly recommend Skyrim too. Thing is, you kind of have to like those kind of action RPGs. Skyrim is made extremely well, and is a super fun and engaging game though.
Just depends on what you are into or want at the current moment, a shooter or an RPG?
That is a great debate! If you have the opportunity get them both!
But anyway, he's right. What are you into?
Are you more of the type where you like to play alone? Are you looking for a game you can EASILY dump 100 hours into and not be done? Do you like medieval/Nordic themes? Do you enjoy leveling up? Do you enjoy intense storylines and and a HUGE world that really makes you feel free and REAL?
Do you enjoy playing online more than playing alone? Are you a huge fan of war games? Do you like being hyper competitive? Do you love First Person Shooters?
Those are the questions you have to ask yourself to be able to decide. I have both Skyrim and Battlefield 3 and they offer me different things. When I feel like not being bothered or the internet is down, I play Skyrim, if I have lots of friends on and feel like being competitive, I play Battlefield 3.
Well, I hope I helped.