There are many aspects in games which I find important.
Strong storytelling is probably the most important one in general, though there are many exceptions to prove that rule.
Player choices that matter comes right after.
Generalizing a lot, strong storytelling is "easiest" to achieve in linear games. The time and effort from the developer to fully flesh out all aspects of a story will swiftly balloon in non-linear games, and with that comes the risk of contradictions in the story, forgetful characters (for all its strengths, this is something which a game like
Disco Elysium has not managed to completely avoid), and all too soon, some story branches which turn out to be shallow, hollow or not fully realized in some other way.
Given the choice between a linear game with a strong story, or that same game with non-linear options and a badly realized story, I'll always prefer the
linear game.
On the "opposite" side, player choices that matter pretty much
have to mean a non-linear story. I mostly dislike truly open world (roleplaying) games, since FOMO leads to completism leads to issues with pacing and being overleveled for the content, but one step down from there - and for many other types of games - lies gaming nirvana; at least where enjoyable gameplay is concerned. The ability to "forge my own destiny", to roam free from constraints, explore emergent behaviour, and feel like I really have an impact on the game I'm experiencing, means I'm a big fan of
non-linear games. All too often, however, I'll find either a shallow main story, or choices that matter for everything
except the main story.
What I love most is the potential of various recent attempts to try and bridge the divide. For example,
Sunless Sea has many short non-linear stories which are told at a very slow pace, and invests heavily in atmosphere to retain the connection and make you care, imparting the stories with a whole lot more whomph then they'd have when told sequentially, one-by-one.
Wildermyth has chosen to focus on building your connection with your characters, creating an emergent "story" - and
Rimworld approaches this same concept from another angle, with the emergent storybuilding being the main concept of the game. Meanwhile - though still not fully completed, and thus potentially not being able to live up to expectations -
Sacred Fire: A Role Playing Game comes with an actual strong non-linear story, with continuous meaningful player choices. This is realized at the cost of game length, graphics and and possibly even gameplay (it goes quite a bit into the direction of a visual novel) - yet all the same it's an audacious step into a very hopeful direction.
In the end, this is not a binary choice. Linear games done well are great. But the potential of the multitude of game-types which would
not be described as "linear" is simply overwhelmingly vast. Many of them will - and have - failed to compare to good linear games. Yet the gems which can be found here are more diverse and amazing than I can comprehend, and developers have only barely begun to explore this vastness - each of them being inspired and learning from previous attempts. As such, the cream of
non-linear games will always manage to steal my heart, and can be my only choice for an answer to this question.