I've been on Lemmy for years now (before it could even federate!), but never really used it because there was nobody really here (and at the time there weren't any good Android apps - that's changed with Jeroba though).
The biggest competitor I've seen appears to be Tildes. I actually got an invite link to Tildes and have been trying it out.
The main difference is that Tildes is focused on high-quality discussion, trying to replicate old-school Reddit - before it went mainstream. Tildes purposely doesn't have memes or cat pictures, and comments are closer to paragraphs than anything else.
I think that's valuable... but I also know one of the big things that attracted people to Reddit were the memes. Not having memes is going to cause a lot of people to not want to stick around.
Lemmy is a lot more loose, so those people will be right at home. The main complaint I've seen from Reddit is that a lot of people are turned off when they see Lemmygrad as one of the most active instances, and they've been associating Lemmy with hardcore tankies.