I know Justice League comes before Justice League Unlimited, but other than preference, does it matter which I watch first?

Even though they're technically two different series, JLU picks up only a short time after JL leaves off, so they feel more like one long series, and events and characters from JL are still very much relevant during JLU. JLU does build on prior knowledge from JL, and just general knowledge about the characters won't be enough to understand everything. And yes, JLU will definitely spoil parts of JL, including the series finale, which changes everything for the team and has lasting effects.

So while it would definitely be best to watch JL first, it really just depends on how much you care about fully understanding everything in JLU. Honestly, you could easily follow many episodes of JLU without having seen JL, since they feature characters and plots that have nothing to do with the first series. However, several episodes would be impossible to understand without having seen JU first, and many events, and some of the character development, would have little impact or significance to someone who had started with the first episode of JLU. There are also many characters (other than the League) who show up first in JL, and then return during JLU, and unless you know what happened during their earlier appearances, their later appearances will be hard to understand.

So it really just depends on you. I always prefer to get the best experience possible when I'm watching something new, and for me, that means watching it in order, so I can fully understand and appreciate everything that's going on. I hate to be watching and feel like I'm missing something, or to wonder what's going on, or who a character is. But a lot of people don't really care about that, so if it won't bother you to feel lost now and then, watching Unlimited first won't be a problem. Justice League is really good though, maybe even the better of the two, so it's definitely worth watching at some point either way.

I'm sorry, I hated to make this so long, but there isn't really an easy yes or no answer to this question, so I felt I had to elaborate a little.

It doesn't really matter. Personally I haven't even watched a lot of JLU, I just watch random episodes which sound interesting to me, I skip plenty of episodes completely and the episodes I do watch, I don't even watch in order most of the time.

And it has made absolutely no difference. I don't feel confused, I can follow the plot easily, it's not hard at all.

Yes, it's made as one big overarching story in some ways, but let's not forget it's a children's cartoon at heart. They didn't expect every child to have seen every single episode already without missing a single one (remember this is back in the days before you could just record a whole series, if you missed something, you missed it) so they intentionally made it so that you could understand every episode without ever having seen the show before. It's not like they made the show so that anyone who hadn't been watching right from the start could just never watch it. Plenty of kids would have only started watching from like season 3 of JLU, having never seen JL or the first two seasons of JLU, and still did just fine with it.

So basically, watch it however you want. It makes no difference.