Game tone is a very important element for immersion. Neither way of playing is wrong; I generally favour dark and gritty myself, but one of my favourite campaigns ever was played firmly tongue-in-cheek, with the fourth wall being regularly mistreated (It was a Hackmaster campaign, and we definitely played into the parody nature of the source material). Where it can go wrong is when different players are on different wavelengths, and where that is easy to solve at a home table (preferably before the campaign starts) there isn't much you can do in public games.