There is no way of completely blocking Facebook and Google data collection. If you do manage to block their million web addresses, a lot of websites would simply stop working because they rely on their technologies. Also, Google will always have some info about you, even if you don't use their services or web completely.
For example, a lot of your friends have your phone number in their contacts list. Most of them probably use Android too. Android, by default, has Google account synchronization turned on. So, even if you don't have a Google account, or you don't use their services, they'll still have your name as well as your phone number.
The point is, no matter what you do, Google will have at least some bit of your data and you can't prevent that.
Now, back on the thread - I'd certanly always choose Chrome over Microsoft Edge. I do use some Google's services, but even if I didn't, I would still choose Chrome over Edge.
Sending full URL-s, including private information, like exact URL hashes are huge NO for me, at least. It's even worse that browser is said to be privacy-consious whilst still collecting what shouldn't have been collected at all.
Besides that, Edge doesn't really offer anything new and what you can't get everything easily in Chrome. It's literally Chrome, with filter like EasyPrivacy and with 3rd party cookies disabled.
