Verizon Galaxy S4 Battery Issue

I bought the S4 the day after it was released on Verizon. It's my first trip back to Android from iOS since the Moto Droid 1 and I love it, the options are vast and superior. However my battery life seems to be very low. For a 2600 mAh battery I'm only getting about 10 hours off charger with about 2 1/2 hours of screen on time and I hit about 30% battery. That's with Mobile Data off, Power Saver Mode On, GPS off, All Gestures off, Wifi On (full service) and adjusted Auto Display. I went to Verizon and they switched out my battery to see if that may have been the problem but it doesn't seem to have helped. I'm currently running Battery Guru to see if it can help assess the situation. My question is this, is it possible that there's a fault in the phone and not battery? Would calling Samsung and having them give me a new phone be worth my while or just more trouble? My main uses are showing Screen at 51% and Android System at 23% (I feel like the OS should not be using up that much battery) Any help or advice would be greatly appreciated! Thanks a lot guys!