I have a US Standard Precision as my #1 bass at the moment, and a VM Squier Precision as back up. I often pick up the Squier at home if I want to try something out, and can definitely feel the difference between it and the Fender. Less smooth, less...something. Both basses have D'Addario flats, both set up the same, but they still don't feel the same. I play better on the Fender, I am sure of that.
(And I know my pic shows me with a Jazz, I still have that, just in a P bass phase at the moment!)