Neutral is the most nebulous aspect of any sport. It is simultaneously the most boring and most interesting part of the game depending on who you ask. Most new players would argue the neutral game is just playing footsies with the opponent until the combos start, and that down time isn't fun. Most experienced players would argue that exact reason is why it's so interesting.
In most of these games, the neutral game will look like long poking buttons, short, fast stubby buttons, or ranged projectiles in an attempt to zone.
Neutral isn't truly 50/50 between the opponents, however. Some characters have defensive advantage in neutral due to the range on their buttons. Axl Low from Guilty Gear and Dhalsim from Street Fighter come to mind.