Basically, as the above states, is a Lvl 10 Grand flourish better than a Lvl 1 Final Flourish? (Or any other 4* to 5* weps) For the speed bar, there seems to be no change (as in, it doesn't increase with heating), but the damage significantly does. (Mainly asking for damage, I get the CTR part to it :)
(Btw, this is for PvP)
It seems like 5* weapons are somewhat weaker than a fully heated 4*, until they reach lvl 4-5. You should use fully heated sets for pvp regardless.