Handheld. I find the buttons to be a lot easier to press because its basically just two triggers when it comes to first person shooters and I don't like how my hands would be seperate if I was using a keyboard and a mouse.
Keyboard+Mouse is the way to go. It feels more precise than using a joystick while aiming. If I'm playing a third person action title, or a racing game, I'll use a controller.
I have used both quite a bit and if you use a computer always use the keyboard and mouse. For a console you obviously use the handheld controller but if you just want preference I would have to the the controller. It allows balance gameplay unlike the computer where some people have a 200 dollar mouse while some actually use their touch pad on there laptop for a first person shooter. So I would say controller but again its different for everyone.