I think a lot of it really does come down to map size.
Larger maps contain more shards by definition.
The more shards the AI has, the more mana they are going to have available.
The AI doesn't snake, so I think it really helps the AI to have nobody running around in its' back lines.
If all the fighting is in border cities, then back in the back somewhere the AI can build shards up to 3 mana per turn each without enemy armies stepping on them and making them start completely over.
On tiny maps like I usually play, there are only border cities and no back lines for the most part. The only way to get a back line is to snake and fertilize nearby ground due to city length. The AIs don't do that, but I do.
A lot of my advantage comes from having a back line when none of the AIs have one.
They have to take cities from me to decrease my mana production, and it's not nearly so hard for me to reduce theirs.
For that matter, the AIs are really good at messing with each other in that way and I usually don't have a lot of work to do myself. They just keep each other low mana without my involvement.
Anyway, I think that map size does really play a large part in how much mana players have.
For that matter I think it has a lot to do with how much of every other resource they have too.
If you are playing on large map sizes and you have some large block of physical space that belongs to you, it probably has all the resources you need in it. If you are on a small map size your little piece of the world is much less likely to have all the resources you need in it.
I have a theory that may or may not be true that how often people CTRL + N varies inversely with map size. Basically, the larger your chunk of the world is, the less reason you have to redo the starting conditions because you are more likely to have everything you need in your space.