I do not have an outdoor grill but would like to make steak. I just bought a grill pan, and I have an electric oven with a broiler setting. Between these two methods which would produce the more tender and juicier steak if I have an already tender steak like Filet Mignon?
If by 'grill pan' you mean something heavy (cast iron) like:
then it would be your choice as to whether you want to heat them on top of your stove or under your broiler. If your 'grill pan' is less heavy duty (say aluminum) then it is unlikely to be capable of with standing the heat required to 'best' cook a steak. When the weather here does not favor outdoor grilling I get great results out of placing my cast iron griddle/grill (similar to the second picture) inside of a half-sheet pan and under the broiler to preheat. Once the iron reaches 500F I will add the steak for about 3 minutes per side (for a med-rare) I would also suggest wiping the iron with a little oil first.
You can also slow-fry steak on your cooktop. This requires quite a bit less heat, but takes rather longer.
I use butter to fry it in and try to keep the heat just below where it will burn the butter (about half on my cheap electric cooktop). The meat probably gets turned a few times more than what most cooks recommend. It's fairly well done when the meat's juices pooling on the top are starting to go clear.