I thought this was really simple, but after a game last night I'm questioning myself based on the Counting Damage Dice rule on Pg. 406 and the massive damage unleashed by a level 4 fighter in last night's game.
A fighter with a +1 Striking Greataxe critically hits an opponent using the Vicious Swing Feat. They are doing 6d12 damage + double Strength mod? Correct?
(3d12+STR)x2 unless the GM allows them to roll double dice instead of doubling the result of the normal amount of dice, in which case it would be 6d12+(STRx2) as you say
They're both the "same", only the normal way is swingier and the double-dice way is a smoother curve of results