Fall of Rome on Prince as Huns seems to have too few turns in it. (Either that or there needs to be a wave to declare peace with the other barbs to allow concentrating more on Rome.)
On Settler level, I'm sure the AI production handicaps would allow the human to double KO as any barb as AI production will suck, but Prince is a high enough level where the Gauls will send a big wave of troops at them (built from cities they conquered from Rome) right after the Huns conquer Constantinople [Greece captured first to get the promotions needed to deal with the tile placement]. That wave contains enough units which cost just enough turns dealing with to make it impossible to reach Rome by turn 70. (Too low difficulty level for another AI to take Rome; the replay of events showed that Franks only reached NW Italy; Vandals only took a few coastal cities; as as for Sass, Eastern Rome actually took back the one city they had captured. Celts a non-factor.)
[My estimate is that I would have captured Rome between turns 75 & 80; and I assume that somebody needs to take Rome to avoid Rome winning a victory as that team won even with East Rome losing its capital and both Romes losing quite a few cities.]
At a glance I'm not sure they really intended this game to be played as anybody other than the Gauls or Franks as those two civs appear to be the ones in the best position by far to succeed in the double KO in a mere 70 turns at Prince or above.
Overall in comparison to the Civ III Conquest scenario:
Starting units / city placement : Civ V much better
Hexes much better
Good idea to disallow barbs building settlers, along with disabling science.
Pre-built roads: For most civs, their both decent. However, the lack of the large neutral roads really hurt the Huns in terms of gold as their starting city while in a production power house location doesn't touch the coast, they aren't allowed to build a settler to found a city on the lake (to open trade routes); it's extremely time consuming and expensive to build a road to the first conquered city.
Score system: Civ V is suffers because it doesn't make it clear what the current score within the game at all is; while the Civ III Conquest wasn't quite clear but at least you saw one of the civs tied for losing the game.
# of turns: Civ III Conquest better; it's better to have too many turns for some playable civs than too few turns for other playable civs.
Diplomacy: Both have problems; Civ III had too few restrictions; Civ V has too many. Both Romes should be in locked wars with everybody (like Civ V), but the barbs ought to be able to have full diplomacy with each other (like Civ III).
The policy system is great. (And the Roman tree is a very good read)