well i wouldnt use the drill with a dremel bit, because it wont go nearly fast enough and is large and unwieldly. id recommend going with a craftsman dremel, just because i got the $20 sears one and although it feels like its about to blow up every time i turn it up fast it is so worn out... but its also probably 10 years old and is used all the time, with sears you can take back a tool even if it is 100 years old... my friend took back a hammer that was made in the 40s because the head popped off and they gave him a new hammer.
drill: very heavy and 1000-1500 rpm
dremel: lightweight and 30000-35000 rpm
of course the drill has way more torque... different tools for different uses.
a dremel is a good investment, i use mine for just about everything, from working on the car to modifying computers to changing out toilets its made odd jobs around the house 1000 times easier. because its a baby sander, hacksaw, shaper, chisel, etc, all in one.