Corded is the best way to go, but then it really depends more on your personal needs. I have both but use the corded 99% of the time unless i can't for lack of an outlet or whatever.
A tip about drilling the airbox tho.... remember, when you grind away at the plastic you'll be creating a ton of fine plastic dust ! You'll neede to clean every spec out of the airbox once youre done or it will end up in your carbs ! And there are a couple holes in the restrictor plate about the size of a golf ball. therefore it's impossible to get any dust out of the area on the other side of the restrictor. So be sure to plug those holes up so no dust gets in. finally, to make less dust cut away as much plastic as you can without the dremel. I used a drill bit and perforated an outline of the hile i mwanted, then finished off the edge with the dremel so i didn't need to dremel too much. Also use the coarsest drum sander barrel you can get so the dust isn't as fine and easier to clean otu and the work will go faster. You can vaccum the dust out if you have a vaccum that'll work for that, plus wet paper towels will pick up and final particles.
as to what brand, i've had 3 dremels and they haven't been all that sturdy. Not saying they're junk, but they haven't lasted as long as they should. The last one tho has been better and lasted 5 years so far. Then again, i have a off brand one at work i paid $20 for thats been just as good so far, so who knows. I'm sure most of the brand name rotary tools are just as likely to be good as the dremel.