It slightly depends on what kind of game you are making.
Generate Server side and transfer to client
If the player can make their own maps, or the map can be generated when a player is playing offline (but can later be shared online), then the best methods would be for the player to transfer the map to other players directly. I remember Warcraft 3 used a similar method, where every player that didn't have the map, would download it as soon as they join the room. I'm not sure though if it was done user to user, or with the server in-between.
It can also work to generate the map server side, and then give the data to all joining players. If the game is too large, then give a part of it to each player, similar to minecraft.
Generate the map client side and verify?
I find this idea really bad. However, it could potentially work, if the maps that the player make are very limited and can be replicated with success. I can't think of an example that this has worked, maybe it has, maybe its just not worth it. At the end of the day, most of the resources have to be on the client's machine for this to work, so the more options they have when making a map, the bigger the final executable game will be (but the less resources you will have to send with your server).
At the end of the day, you are only sending a few data that describe the new map, you are (most likely) not sending new assets as the new map is using assets that already exist in the client's game, so the resources sent by your server aren't that big. An html website is far bigger than that, and you can navigate to them almost instantly.
