Having only watched a couple episodes of Firefly and the movie Serenity, I wouldn't say "better" but different.

Serenity/Firefly is slightly softer sci-fi, while I'd say The Expanse is fairly hard sci-fi. Expanse, at least in the books, they actually go weeks and months in space between stops and make it a point to tell you; while from what I remember in Serenity they treat going to another planet as going on a couple days road trip.

Firefly is better imo, but it does have the "advantage" of only having had one very good season. Would Firefly have kept the same quality or better over 6 seasons? Who knows. We've all seen shows with excellent first seasons that later drop in quality (Altered Carbon for example). Regardless, The Expanse is a great sci-fi show that is at least worth trying out if you liked Firefly.

The boner the internet has for Firefly means I’ll get dragged for this, but The Expanse was by far the better story overall.

That being said, I enjoyed Firefly a lot. But the world building, character arcs, political intrigue, etc was just immensely more immersive in The Expanse. Especially goes if you read the entire series. The show was great, the books were also great and well, expanded, the story. Highly recommend.

I wouldn't bother pitting then against each other. They're very different, but if you like Firefly, you should check out The Expanse.

Personally, though, I recommend the books. I watched the first few episodes of the show first and was underwhelmed, but then checked out the books and was hooked right away.