6SN7 vs 12SN7

I don't know about the 12's, but my Cayin integrated amp uses both 6sn7 and 6sl7, and they sound wonderful (brand specific as you say).

If there is no great reviews for using that 12 type I would not change jumpers.

having said that, how many tubes, how much will it cost to try both yourself?

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Brent Jesse let me return tubes I didn't like and try a different set which I kept.

You have ___ type now?

Order the other type, listen (break them in, simply leave amp on, no content just on, for 60 hours), decide, keep, or return and get a spare set of your existing type, maybe a brand that sounds even better!

The 6 and 12 volt heater versions sound the same. You can probably pay less for the 12 volt version because they aren't as popular. Same when I needed a quad set of 12V6's for one of my tube amps. They were half the price of the 6V6's.

as old stock tubes go 6sn7 octals are still relatively plentiful as many many many were used in mass market television production - they are still relatively cheap and the us made ones by ge sylvania and rca (under various brand names) sound very good, very spacious, and are usually well balanced side to side, no need to pay nosebleed prices for these and the common variants 

I have a tube preamp that has a switch for 6 or 12V heater and I have several 6 and 12SN7’s. To me they sound about exactly the same but I swear my mind tells me the 12SN7 has the edge, they just sound a little better to me.