Some seed bags are fertilized. If you used such a bag, this could be causing the excess growth. If you still have a bag, or can find it in the store again, you can check and know for sure. If this is the cause, the fertilizing effects probably won't be there again in spring. Definitely not after next summer. You could begin a fertilizing regiment for your entire lawn, and it will all probably even out eventually.
Also, your old lawn may be in need of some care, like thatching and aerating, which might bring up the color and growth. Your new lawn was likely planted on recently mixed soil and doesn't have to compete with detritus and weeds. Your new lawn might not be growing faster; it could be that your old lawn is growing slower. If this is the cause, give your old lawn some TLC, and even toss a bit of fertilizer on it.