Quote The Elf:+1, especially if you are using semi-pro gear. Expander will probably sound more natural. Home studio gates never worked for me because the attack was never right, I was always unhappy w results.
I frequently gate first, but I'm only looking to reduce the spill, not silence it completely. In fact I more often use an expander than a gate.
However, I also worked a lot in nice rooms, with Kepex II gates . Those can actually gate a snare nice and tight, and let you set as much release as needed. BUT , ymmv, as the drummer must be consistent to always hit similarly.
Gear list: If you can't find it, grind it