If you're using Google for searches, it also doesn't matter if you use Firefox or Chrome, obviously they have access to the full queries you do on their properties.
It does matter becauae you can use an anonimizer for seach on Firefox just fine, but if you use Chrome then Google can collect everything you enter in a form and see where it's sent. Not sure if they do, but they could. One element of security is comparmentalization: avoid using a client and server from the same adversary, if you can, to minimize correlations.