will a stock integra type s beat a stock holden commodore vs ute in terms of speed?

i have a 93 acura integra with a ls vtec motor swap...well i got a s1 tranny on my b18b1 ls vtec but i think my tranny is broken cuz sometimes with i shift it doesn't want to go in 1st & 2nd gear but the rest work fine and i recently replaced a new clutch but still having the same problems...so i decided to change the tranny.one of my brother friend gave me a a1 tranny for free and i was just wondering if i can use it for a replacement on my b18b1 ls vtec?

integra type s?? no such thing and quit bench racing just go out and do it...a1 tranny for B series?? i dont think ive ever heard of it...if its all motor get a b16 tranny or a ITR tranny if you can afford it

* acura rsx type s