There are two practical differences.
The stainless gun won't rust as easily. Duh.
The blue gun however has an advantage if you ever want to swap the barrel over for a caliber conversion. A blue setup is easier to unscrew without ruining the threads on either the frame or barrel. Unscrewing a stainless setup is iffy because they can "gall"...basically the threads can become useless.
Note the words "can". But this is why you see more caliber conversions on blued Ruger single actions than stainless, and why I bought my 2005-era New Vaquero in blue as a 357Magnum knowing that as a tinkerer I was likely to one day swap barrels. I did it, too...it's now a true 9mm (.355" spec, Douglas Premium blank).