I prefer free exploration for both world maps and levels. I just really enjoy exploring areas, not much else to say about it. That's not to say linear cannot be a good thing, I still enjoy games even if they are linear, I just prefer a more open world is all.
Fee exploring & wide map area's (like Paper mario Sticker Star.). Otherwise some linear maps aren't very fun for me. Others are alright as long as the story or game play makes up for how linear the exploration is sir.
Probably free exploration, as enjoyable as it is to go just from point A to B, it's also nice to be able to get around and grab some goodies along the way.
I like maps to be free exploration and I like the levels to be a mix of free exploration and linear since there good anyway there made for the most part.
For world maps, I would prefer a linear storyline with some free-choosing moments, but with a free exploration world map. As for levels, linear. I don't think I would be able to fit up with free exploration side scrolling levels.
See, I actually really enjoying playing non-linear sidescrolling games like Metroid and Shantae. Those types of games are really enjoyable to me, so I don't see them as a problem at all myself.