They can co-exist - they don't have a single team member in common, other than possibly Champions Reinforcement Roster member Prodigy, who hasn't made a physical appearance there and therefore could in theory be the other Prodigy (one of the Slingers) and not the ex X-Man and YA (Zub has even avoided answering the question of his identity when asked on his Tumblr AMA).
The Champions are more of a replacement for the New Warriors than the YAs, quite frankly (and they DO have a team member in common, Nova). The last NW volume was at around the same time as the last YA one.
And don't say Marvel should only have one teen team at a time. DC had two Titans teams until this week when one of them ended, and also have Young Justice.