If you are not currently eligible for an upgrade then you cannot go to any other site to upgrade. They still go based on your upgrade date because vzw is the company that provides service to you.
If you technically could upgrade and you had a discount through verizon the other sites will not provide you the upgrade discount verizon has. That is only an offer that verizon provides you.
In regards to being able to change your plan online it is still possible. The only thinh is that you have to make sure the other website didn't require you to have a certain plan for a certain amount of time. For example, I know wirefly sometimes requires you to get a certain plan for a few months and if you.change it they will charge the full retail price of the phone to the credit you used.
I used to work for Verizon and i always saw that a lot of people had problems when going with a different vendor. Because of this i will never buy a phone that is not from verizon directly.
Keep in mind they could possibly have different return policies and different restocking and early termination fees.