Battlemaps are good if you're going for a swashbuckling or strongly tactical feel. I like to say 'your players can't swing from the chandelier if they don't know there's a chandelier.'

Battlemaps are great for a certain aesthetic (in the the game design sense of the word) because they allow you to add things for players to improv with without explicitly enumerating a static set of options. If you draw the inside of a tavern, when the tavern brawl breaks out they may do something that surprises you; "Can I throw the bottles at him/flip over the table/dive behind the houseplant/throw him out the window/etc" Whereas theatre of the mind requires your player to either intuit that there would be a bottle on the table that they could throw, or you to explicitly say "and there's a bottle on the table in front of you." And if you tell them there's something in front of them, they will laser focus on it and never even think to flip the table/dive behind the houseplant/etc.

Theatre of the mind is good for games that put the emphasis elsewhere. If the focus of your game is on entrigue, or courtly drama, or in a setting that's highly improvised, that's when theatre of the mind shines.