I have used both. Service wise, both were fine (we had FIOS) and equal for the general population.
The problem we had with verizon was the billing system!!! the bills were crazy and EVERY month they were wrong. It took forever each month to correct and each month they said it wouldnt happen the next on. Their computer system for the customer service reps were terrible and they had so much trouble trying to help us. Also, their line items on the bill make absolutely no sense so deciphering where they over charged you is a nightmare.
Finally, my husband got fed up and switched us to Cablevision. We got a similiar deal price wise, plus a $300 gift card to PC richards. We havent had any billing issues.
I also used Cablevision when we were in Brooklyn and had no trouble there either.