Not surprising to be finding a 100% saying they're looking for "a bit of both" in photos here, for there's even more things you might like in a photo apart from the two you're suggesting, Daniel - which goes with what Himalayan is saying, too. It can be the uniqueness of a situation/face/pose, the creativity, the "eye" for things, the colours, the "drama" that can best be captured without colours (goes with technically well done b+w photography, of course)... and sometimes the photo as such tells a nice story, but technically it is not so well done - even technical bloopers can be photos that are particularly appealing... there is soooooo much in photography, it is such a wide field, that it is really, really hard to tell.
I try to figure out what the photographer is trying to do, and then evaluate it on how well they have acheived this. There are so many things that can be done with photography, it's hard to limit it just to a few points. This is why I like some comment by the photographer explaining the image. For instance, I don't expect and abstract composition to tell a story. Nor do I need a documentary photo to be technically "perfect" if it tells a story well. If I see obvious things that I think should be corrected, then I point them out, but I allow a lot of artistic license. Often I voice my opinion on how I would have done the photo, but that doesn't mean my flavor is the only "right" way to do it.
Also try originality. I hate seeing the same type of photos Everyone has their own opinions. Like I find lines interesting. I don't know why I just like them a lot! Of course, it still depends. I won't like any line pattern I see.
