My preference is sticking with the sequential turns; admittedly a few things outside of war could have an impact, like two teams researching a tech or building a wonder on the same turn, and the game (randomly?) chooses between one. This is less likely with epic speed but it could still be possible if two teams, say, start off researching for buddhism.
That isn't any better if your team is last in the turn order is it
I'll split the next paragraph into severl chunks to better answer it for you Earthling.
The main thing I still don't like in simultaneous turns is actually a huge artifact of the CIV combat system (this particular thing I'm not a fan of at all, btw) that has a major impact on gameplay. Namely, the way units heal is really dependent on sequential turns in the game.
No, all units heal between the two movement portions of adjacent turns (so move units-> end turn -> heal -> next turn), or when you promote them, but units can't use XP gained in that turn for a promotion unless they already have much XP for a promotion (so if at the start of the turn they could promote to say, shock, then you lose a battle and then they could prmote to both shock and cover, they can take both promotions and the corresponding healing bonus). However, while you can't move units after you have ended your turn in sequential pitboss, I was under the impression that you could promote units even though it was not your turn due to game mechanics. If I'm wrong, then you have a fair point, but if I'm right there is no issue between the game types.
There are cases where it doesn't matter if you double move or not; simply having simultaneous turns can wreck a war/battle (double moving of course would make it worse). For instance, if two stacks come across each other, the one who attacks first does a bunch of collateral damage with seige.
This would be covered by a double move; the stack that moves last would have to attack last unless they moved right at the start of the turn; however, siege units are immune to collateral, so you can collateral them back. This does favour the defender, but no more than a sequential game; the the team attacking has to move next to a stack or city before they can attack, which will always give the defenders a chance to collateral the stack in the first place.
In open field combat, stick to the hills and forests, make your opponents move next to you first (stay two tiles away, make sure all defensive positions have no forest next to them etc.
In sequential turns, the defending side would get a heal in before the start of their turn; this doesn't happen in simultaneous turns!
Non sequetur, the attacking stack can always attack with the catapults and immediately attack with the remainder of the troops in the same turn never giving the defending stack a chance to heal...
Instead, in the very worst possible situation, the defenders can't counterattack because they are weak, then the attackers get to heal/promote and it's their turn again!
non sequetur; the defenders got injured by being attacked, the attacking units have to wait a turn to heal from teh promotions, so the defenders also heal at the end of the turn/start of the next turn before units are moved (unless you move them).
The same thing applies to units being built in cities; say one team slaved a new unit; there can be a situation where the new unit is then ready the next turn, without having been damaged or attacked on defense. I know this calls for a post somewhere else, but I've always disliked how healing happens at the start of the turn opposed to the end, when everything else happens. Regardless, unless I'm wrong and the mechanic is altered in simultaneous turns, this could have some major effects (namely, the team who gets to go "first" at the start of each turn-usually the aggressor who started the war, has an advantage).
All units are built at the end of a teams turn, so this issue will exist regardless of whether it is a sequential or simul turn game. It's actually worse in a sequential turn game; if you are being attacked by the team after you in the turn order, you can slave a unit and it will be built when you hit end turn, so while it won't have any promotions, it will be able to defend against the other team. Healing I've already addressed.