The downside,
1. You can ALWAYS use your own modem and router with Cox, with Verizon, you HAVE to use their equipment. If it fails, well, too bad, so sad.
2. While internet speeds are not guaranteed, they all say "speeds up to", see what people are getting as an average for the speed you are signed up for, run yourself a few speed tests, then see what people who are using Verizon are getting. A family member is signed up, with Verizon, and their up to 1000, is averaging 225.
3. Check and see what you are required to have to get the 35 a month. Most of the time, you have to have their cell service, auto pay, and I think you mistyped, 1000 is FAR more than 35$ a month.