Should I play mafia 1 original or remake?

I've played both. Quality of life is way better in the remake (who thought Reload should be bound to L?), and IIRC you can adjust the driving physics so you can decide whether you want a realistic or more arcade experience.

In either event, good luck with the race car missions

I think the original has a better atmosphere, you have to drive between the missions instead of being teleported to the location, which inevitably works towards the immersion. But it also an early 00s game, sometimes it can feel too hard or frustrating. See it for yourself if that's what you want.

The remake has much better gunplay and graphics, and overall has been 'smoothed out', but personally I think the new casting choices were unbelievably bad, and take all of the soul out of the game.

If you can get past the jank of the original (and get the community patch to add the old music back in), I personally think the original is the better game by far, but I was a huge fan of the original, so I'm biased.