The second, scissor-type one is by far the best. The first one is called a guillotine style clipper, and the big problem with it is that when you apply pressure, the blade forces the nail up against that little loop, causing discomfort. With the second type, the pressure is coming from both sides, so it cuts through the nail more quickly and with less pressure and pain.
The dremel is the best, but if you can't do that then definitely use the scissors type clippers.