Question

What's the difference between this, pokeBase and battle subway?

Answer 1

Pokebase: the main area for general questions about Pokemon, for example help with the gameplay, how moves/abilities and other mechanics work, competitive battling (except teams), plus the anime and TCG (though we are more focused on the video games). Pokebase is sometimes used to refer to the entire community area.
Battle Subway: the Rate My Team (RMT) section, for posting competitive battling teams. Teams must include all Pokemon and all relevant information.
Meta: the place to ask questions about this site itself, for example how to use a feature of Pokebase. Suggestions for Pokebase or PokemonDb (e.g. improvements to the pokedex) can be made here.

Source: The Rules Section

Answer 2

The PokeBase is for normal, general Pokemon questions, such as "Where can I find such and such item?" or "How do I EV train?". This is the main section that generally gets the most attention.

The Battle Subway is for competitive Pokemon teams to be posted and rated by other members of the community. Competitive means no in game teams, though!

The rules page explains this in more detail.