I bought a Jobmate (Canadian Tire) rotary tool for $12 a few months back. Worked great until I accidentally pressed the chuck lock while the drill was under power - the cheap plastic lock ground down in no time, so now I just use that rotary tool for cut-offs, since the cut-off collett is what was stuck in it at the time. As long as you don't do what I did, I'd recommend it considering the amount of tool/$ you get. However...
The local Liquidation World (they probably have locations out your way) had two rotary tools for sale. One was a Black & Decker for about $25, the other was called a Tool Shop. I've never heard of Tool Shop before, but it was only $16 and it came with a hanger and a flex attachment, which has been extremely handy. To answer your question, yes, Dremel brand bits etc. are interchangeable with tools of other brand names*. For that reason alone, buying either a Jobmate or a Tool Shop tool is a wise investment, because each comes with about 30 or 40 assorted tools. The Jobmate cut-offs are a bit weak, but four or five of them were enough to cut through 1/4" steel tow-hitch clips on my car (a total length of about 6"). When you work that out to $0.40 to get the job done, it's a good deal.
The other bits that came with the Jobmate and the Tool Shop are outstanding, and although I can't say from experience because I've never used Dremel bits, I'd say at least close to being on par. Suffice to say that I'm very, very happy with the value of the Tool Shop, and if I need more cut-off or grinding bits, I might even buy another Jobmate, since $12 is almost as much as a pack of Dremel brand cut-offs alone will cost you.
*I should mention that I don't know how compatible the Dremel drill-press attachment is with other brand tools. I've wondered that myself a few times, but if not, I think I might make my own sort of press for the Toll Shop flex attachment.