The danger of a linear game is that it may leave the player feeling powerless, like s/he's just along for the ride and doesn't really have any control. The player feels herded and restrained, and it's not a very fun experience.
The danger of a game that's too open is that the game may feel aimless. Presented with so many choices, it's hard to feel like any of them have much meaning. An NPC says, "Hurry up and do this story mission," but the player wanders around doing whatever s/he pleases with no real urgency. It leaves the game feeling unfocused and detached.
The trick is to strike the right balance between the two extremes for your game, then mix in other elements that combat the weakness of too much openness or linearity. If your game is linear, take measures to ensure that the player feels powerful and free, rather than strung along by the game designer. If your game is open, make sure to give the game a sense of structure and meaning, so that the player doesn't get lost is a sea of choices, indecision turning to apathy.
"The worst part about these reviews is they are [subjective]--and their scores often depend on how drunk you got the media at a Street Fighter event." — Mona Hamilton, Capcom Senior VP of Marketing
*Image indefinitely borrowed from BrainBoxLtd without his consent.
