How much does the transport affect sound quality?

As far as telling you what kind of differences you'll notice, I really can't. Its no different than matching any other component. Different transports will sound different from each other.

There is one thing, though. Sometimes its beneficial to use the same brand for your transport and dac. If the same designer made both pieces, they're usually meant to work together. Some even take it a step further and use proprietary designs. Wadia, for example, has a feature they call clock link. But to take advantage of it, both pieces need to be Wadia.

Transports certainly contribute to the sound of a transport/dac combo. For the good or bad depending on you system and DAC, so I agree with Zd542 that using the same brand for each piece would probably be best. BUT, if you are going to do that how much would you really benefit and wouldn't a good quality CDP be as good. Maybe not, but I bet it would be hard for many folks to differentiate.

Transports do make a difference as well as the power supply. The cleaner the power the better the transport will sound. I use a modded 47 Labs Flatfish with a 12v linear power supply and a custom SLA battery supply. With the linear supply the FF sounds nice but the battery opens up a whole new sound scape. A clean robust power supply is a good 80% of the sound you hear.

Just my 2c

R