I feel like I missed out on the Burnout 3 love because my first intro to "modern" Burnout was Revenge when I eventually got a Xbox. I skipped 2, and 3 never made it to GameCube for whatever reason. So for me, Burnout 3 feels like a step back due to the lack of same direction collisions. I understand that that's generally not the opinion of series fans, that partially taking away the danger of crashing simplifies the game too much. I like the added options in weaponizing your car however. I'm not a huge fan of pure car combat games, so Burnout Revenge is the perfect "your car is a weapon" racing game for me.
I love the handling model in Burnout but lets be honest - F-Zero GX is way more mechanically demanding. I personally don't mind brake-to-drift systems - I fucking love Hot Pursuit 2010 - but the challenge in Burnout is survival and course perfection. F-Zero GX has that plus the quirks of its physics system in snaking, track skipping, hitting the boosts at the edges, etc., etc.
I'm not a huge crash mode person. That may influence the results as there is a beauty to that mode which does play with the physics a little more. But I buy a racing game to...well, race.
If it was Burnout Revenge, it's closer for me. If it was Initial D Special Stage, it's a coin flip. But between these two, it's F-Zero GX.