If you loved Firefly (I also loved Firefly), you'll love Buffy. There's a great balance between funny moments with clever writing, and taking things seriously to move the plot along.
The characters feel like people we all know without being stereotypes, and grow over the course of the series. The spooky-woo-woo MacGuffin stuff isn't overly contrived usually, and when it is, it's supposed to be like that. The show is an ensemble show, and so dynamics that swirl around a group of friends, for good and for ill, are what keep is grounded. Story arcs are clear and planned, and not every character is safe or safe to be around. There's a whole, expensive cinematic universe that develops over time, all ultimately built around the concept that life is complex and you can't just punch your problems in the head and expect them to go away.
I will say that the series had a shoestring budget to start, so Season 1 is bare bones and a bit rough at times. Season 2 is not my favorite, but Seasons 3 and 5 especially are some of the best television that has ever been. I've never seen Supernatural, not even an episode, and have no desire to do so.
Edit: I'll add that once you get invested in the characters, the show leaves an emotional impact on you. There's a couple episodes that when I see them on TV, especially one in particular (some of y'all know which Season 5 episode I mean), I simply won't watch because they're too real and will just change the trajectory of my day.