i never had an n64 for mario cart but i did have a ps1 back where i lived, and battle and chase was my all time favourite because of its crisp and vibrant 3d world and race cars which you can fully customize, and also for the verities in the racetracks that i think puts it far above that of mario kart's half 2d flat racetracks itself.
i remember that the controls were a lot more tighter compared the odd n64 controllers so you didn't have to bank left and right only to watch your race cart skid to the side and smash into a wall, the game is easy to pickup and play and unlike mario kart you can actually have fun and win some races without having to learn how to slide like a pro! i found Battle Chase to have aged better because the tracks and cars are all very detailed and well designed, even by today's standards if you look at the game worlds itself you'll noticed that there's some very cel-shading looking 3d models in this game which i rekon still looks absolutely brilliant to this day! also the only time when bass and duo actually makes an appearence in 3d is in this game and this game only. (though i could be mistaken but i'm fairly sure) and being able to have bass and duo's race car is worth the purchase price alone i assure you, where on the n64 with mario kart it's just a single half animated 2d spirte sliding across on a flat polygon surface.
and did i mention how great and electicfying the music in this game are? we're not talking about midi sound chips here i'm talking about the real CD AUDIO experience of hardcore rock and roll that only the ps1 can do! in short the game manages to deliver a fun and authentic racing experience in a 3d megaman world that looks and feels like the classic 2d megaman and i love the feel and thrills of speed where you can see the gameworld just whooshing by as you go, and you can tell the actual distance between the next turn and your car due to the longer draw distance. i only wished that i bought a racing wheel for it before the console broke but i was such a cheapskate that i kept using the first generation PAL controller. i do have a ps3 racing wheel now but my game disk is long gone so i probably have no hope of ever playing the game on the console ever again.
anyhow, i love battle and chase! great game, don't think we will never see anything like that again!