I would say both are pretty known in the web hosting industry. I used Liquid Web not as a web host, but I used to lease my Cpanel license through their company. I think both would be solid choices for what you need. I guess by bigger you mean who has more clients, I can't answer that, but they are surely not your fly by night web host. They've been around for awhile.
You can try emailing their sales team and perhaps ask them that question directly, how many clients are you hosting to get an idea of which one is really bigger I guess, or you can ask other questions in regards to how many employees they have etc, as I'm not sure what your definition of bigger is in this case.