I voted both. I think if executed well, I can get the same enjoyment from a game whether it's linear or open-world.
Here's a great example that happened recently; a friend of mine wanted me to try out Spiderman on PS4. I've heard a lot of great things about the game, so I went ahead and played it for about an hour; but by time I was finished, I wasn't very impressed. A part of me thinks it was because I didn't start a new game, I just began to run around in my friend's game where he was about halfway through it. Using webs to swing across the city, and pulling off some cool feats of athleticism that only Spiderman could was fun for awhile, but I grew tired of it after 15 minutes: proof that I didn't get immersed in the world at any point. So then I went down to the streets thinking there would be NPCs there I could interact with to get a sidequest from - I couldn't interact with any of them. Finally, I found a combat mission where I was in a warehouse fighting waves of enemies, but I had no idea what I should be doing really. I'm the type of player that needs to play a game from the start, that way I know how to best use all assets available to me.
I walked away feeling like I would probably get bored with the game if I bought it for myself: it was a huge miss for me, and after this experience I don't know if I'll ever buy the game for myself.
Later that day, I started to play Metroid: Samus Returns and I enjoyed every minute of playing it.
On the otherhand, earlier this year I started a playthrough of The Elder Scrolls: Morrowind, and I managed to get immersed into the game. Every aspect of it that I've played I have enjoyed, whether it's doing a side quest, tackling the main quest, or aimlessly exploring the world - I've loved every bit of it so far.
To conclude, there are many factors that go into how I recieve any type of game. Perhaps if I started a new game of Spiderman I would have gotten involved with some aspect of the game, but because I didn't, I never managed to get that hooked feeling that I've gotten with other games.