I like the Conquests, but only because I already played "normal" Civ3 a lot.
Conquest tend to be very easy and in favor of the player, they are very dependent on your chosen Civ.
They recreate a very nice historical feeling, but there are often flaws that can be annoying.
Rise of Rome (Romans), Monarch: This was rather interesting, but a bit tedious in the end to get those missing % and tiles of land. Needed some time to finish this.
Middle Ages (Danes), Monarch: Those VP bringing Relics are overpowered. Grab 2, you probably do not need a third, ship to Jerusalem and the Game is over... 6 hours.
Age of Discovery (Spanish), Monarch: You can even be the nation with the least ships, there are several flaws:
-> AI sucks in naval invasions. Not even in war my coastal cities were attacked or troops being transported to America.
-> once you have your mines running, you should declare war -> otherwise you will get too quickly 35K VP. 1K VP for each Treasure, simply too much - mines give treasures every 3-10 turns. I had much more treasures than military units and ships, my only problem was transport logistics.
-> The English will reduce Piracy to zero. All French Privateers and mine were quickly destroyed by either Manowars of different Nations or Elizabethan Sea Dogs.
They could not do better for me - I could cross the ocean without any danger... the Portuguese can even hop from City to City and use their small Island to never have to stay outside a safe harbor at all.
I really like the Conquests, even if they have sometimes real shortcomings.
But while the thrill is that you know the setting and the era, this is exactly why a normal Civ game is my choice, if I would have to decide whether to play only Conquests or normal games.
You do not know where to find ressources, not what enemies you might expect and probably not even if on a continent or an island map. History can be very different and a completely new experience. I think the epic game is also more challenging - most Conquests and their specific victory conditions, often based on bringing something somewhere to get VP, is often rather simple and makes for a shorter game.