For Itch.io, I'd say it's better free.
Other stores, like steam, would say with a price.
I have an indi paid game, between 100 - 200 sales on steam, on itch it doesn't even reach 10 (note, I'm not complaining, I'm just commenting the numbers).
To publish on steam, you must pay a fee and meet several requirements, if your game is free, many people will think that it has some trap or that it is a poor quality game.
On itch, the vast majority of games and game consumption are free-to-play indie games. People do not see bad, that the game is free, on the contrary, it is precisely what they are looking for.
What you should not do is place the same game with a price in one store and free in another, otherwise a group of people will feel cheated.