At the lower levels, you're more likely to achieve bonuses like "killing spree" for killing a number of enemies without getting hit, or "rampage" for killing many enemies in quick succession. The enemies also go down easier.
At the higher levels, you more than likely won't be getting as many bonus points, but the enemies are all worth more. However, the levels become far more challenging and the waves take longer to clear.
I mention "round 15" because that's the minimum round you have to play to on every Spec Ops: Survival map in order to unlock an achievement. There's nothing magic about this round otherwise.
If you're in this for experience gain or for the achievements, there's really little benefit in forcing yourself to play the higher levels, or being particularly disappointed if you fail. It can be good practice or a fun challenge, but I wouldn't feel pressure to survive every round unless you're trying to beat your (or your friends') high scores.