can you set a breakpoint that activates when a register points to a specified value, like eax="abc" ?

psyCK0: forgot to login ?

nope, it is not possible because OD must check the registers on every instruction -> slow.
you can use conditional breakpoint on a specific API to break when [EAX]=="abc"

This may sound stupid, but what exactly would be the difference between register and memory breakpoints, speedwise?

Memory breakpoints can be done in hardware (ollydbg does not interfere until breakpoint is reached). Register breakpoints must be done in software at the end of every instruction execution.