My advice? Don't "threaten."
See what your best options are if you were to leave comcast. Include everything in the cost - so if there is a $60 install fee for Verizon fios, and $60 in equipment you would need to buy, and they have a 1 year intro for $40/month, your price to beat is $50/month. If you think switching might be a hassle, then also give yourself a buffer for whatever you think it is worth to not switch. If it's no hassle, the price to beat is $50. If it's worth $24 to you to not switch, then your price to beat is $52/month.
Then call comcast, tell them your deal is about to be up, and you want to see if they can do anything to lower the price come April (or whatever month your deal is done). Tell them you've been happy with their service (if you have been), but you've looked around and you can get a better deal elsewhere. See what they come up with. If it is nowhere near your $50 or $52, tell them you are looking at $50 from Verizon and ask if there are any other options to lower the cost. If they can't get to a good price, express your gratitude for their attempt, and politely cancel the service and call to set up your new one.
Did this with Verizon recently and they were able to strike a good deal, it was a really pleasant call, the guy was super helpful. They even told me what moves to make in another year to maintain the same rate, which would change if I don't cancel some ancillary service that currently creates a bigger discount when added.