First, please search the FAQ of the games and the forums for questions which you will encounter when you first play Urban Rivals (this question is asked at least once a month on the forums).
It depends on the star count of the 2 cards. The card with the lower star count will win if there is a tie in attack (after abilities / bonuses / Leaders ) .
For example: I play a
Wardog with 5 pillz ( 48 attack ) . My opponent responds with
Cassandra, also with 5 pillz ( 48 attack ) . My
Wardog will win the round as his star count is lower ( 2* vs 5* ).
Now your next question will be, what if two star counts are the same ?
-> The player who "attacked" in the ROUND, will win the round. "Attacking" is where you play your card before your opponent in the round; so here's an example:
I play my
Wardog with 5 pillz ( 48 attack ). You respond with
Wanda, also 5 pillz ( 48 attack ). Now, because I played my
Wardog first in the ROUND (not the match!), I will win the round.
Supposing you had played your
Wanda first with 5 pillz, and I responded with
Wardog 5 pillz, your
Wanda would win...