Not necessarily. The 12AX7A tubes that are designed for low noise can sound better. The Tube Store has a chart about the currently available preamp tubes and their comparative performance.
http://thetubestore.com/12ax7review.html
Also, it is common to get a low-gain ultra-clean tone by swapping out a #1 preamp tube from a 12AX7 to either a 5751 or a 12AY7 (the original Fender tweed preamp tube). But be careful, as the internal impedance of tubes can affect the circuit. For example, you may not want to use a 12DW7 in the #1 stage, but it can be good, depending on the amp circuit, to use it in the #2 position to buffer the internal impedance going to the phase inverter.
http://thetubestore.com/gainfactor.html
And yes, tube rolling is really fun. For example, on my BillM modded Blues Jr guitar amp, I use 3 X 12AX7 for a "mini-Marshall" tone, and 5751, 12DW7 and 12AT7 for "vintage tweed" tone.