With current technology, really the only difference is that an internal card will not use up one of your USB ports, and a USB dongle will not use up an internal PCI slot, so it's up to you in terms of which is the more plentiful resource on your computer.
It's feasible that someday, connection speeds will be so great that they exceed USB transfer rates, but we aren't anywhere near there yet, so in terms of speed they're pretty much equivalent. Some people just prefer not to have a little stick poking out of their computer whenever they go online (and thus choose internal), and some other people like to move the wireless capability from computer to computer, or have it easily removable in the case of supervising internet usage of a child (and thus choose USB).
One other difference is that the cards often have removable (and therefore, upgradeable) antennas – Joel Coehoorn – 2010-08-29T01:06:16.500
1While this is true, I have never met -anybody- who has upgraded just the antenna of his wireless card. To be quite honest I don't even know where you would buy just an antenna. – Mala – 2010-08-29T01:10:59.097
Correct me if I'm wrong, but aren't internal wireless cards genearlly faster? – James Mertz – 2010-08-29T01:29:02.747
Unless your internet connection exceeds 480 mbps (it doesn't), the bottleneck will be at the network level. USB devices can transfer the data to the computer MUCH faster than the data can be received from the network. Think of a long road whose speed limit increases from 60 mph to 3'600 mph or 16'000 mph right before the end. Cars will arrive at exactly the same rate (# cars per second), and the increased delay before the first packet arrives is on the order of 0.00000015 seconds. – Mala – 2010-08-30T01:17:35.583