I think a protagonist should be strong.
Right from the first time we see Kirk in TMP, he's determined to get his command back. When the Enterprise first stares down V'Ger, Kirk disregards Decker's warnings -- sticks to his instincts -- and V'Ger doesn't destroy them.
When we first see Picard in GEN, he's on a holodeck program, then he finds out his family on Earth died, and then he ends up a mopy, crying mess. It's completely understandable that Picard would be in such a distraught state but that's not the the type of character story you should tell when you're introducing him as the person who's supposed to replace Kirk. Then Soran beats up Picard and he has to get Kirk to help him out. When the chips were down, Picard had to call 1-800-GET-KIRK. After GEN, they over-corrected by turning Picard into some Macho He-Man. Kirk could throw a punch but it's his ingenuity and on-the-fly thinking that always saved the day.
Then there are Spock and Data. When Spock first appears in TMP, he's attempting to undergo Kholinar. He's not himself because he's trying to become what he thinks is better. Then he realizes, after melding with V'Ger that he was pursuing the wrong path. In GEN, Data isn't himself because he does something stupid -- like pushing Crusher into water -- and then has the emotion chip installed which makes him act even stupider. It was supposed to be funny but it was trying too hard.
And there's the destruction of the Enterprise.
In TSFS, the Klingons have the Enterprise at a disadvantage. The ship only has five people, automation is knocked out, and the Enterprise still hasn't been repaired from TWOK. As Kirk said, "So, we're a sitting duck." He destroys the Enterprise himself to keep the Klingons from seizing it and escapes to Genesis to figure out what to do next. He's staying one step ahead of the Klingons even if they have the upper hand. In GEN, there's a coolant leak in the warp core and then BOOM! That was so stupid. Couldn't Geordi even try to eject the core?
Finally, the message. The 20th/21st Century vs. The 23rd/24th Century.
TVH handled it better. Spock's deadpan delivery how "Judging by the pollution content of the atmosphere, I believe we have arrived at the latter half of the 20th Century", McCoy complaining about how it's a miracle we ever got out of the 20th Century, Kirk telling Gillian about how he could take the Whales to place where they'd never be hunted, and playing up for laughs the fact that they don't use money in the 23rd Century by having those scenes where Kirk has to sell his glasses for cash and then the exchange between Kirk and Gillian. "Don't tell me they don't use money in the 23rd Century." "Well, we don't." It's all light, funny, amusing, and doesn't make you feel like they're beating you over the head with anything.
Compare that with FC, where Picard says they have a more evolved sensibility, then starts to act like Rambo. When Lily says he envies him for the world he's going to, I don't buy it. If I were Lily, and my only glimpse into the 24th Century was "Captain Ahab" vs. The Borg, I wouldn't think the 24th Century would be any better than the 21st, and Lily was right to call Picard out on his bullshit. When you finish watching TVH, you think the 23rd Century is a better place. When you finish watching FC, you don't feel the same way about the 24th. This wouldn't be a problem except for the fact that Picard wholeheartedly believes something that clearly isn't the case.
This is just scratching the surface but I don't think TNG translated as well to the Big Screen as TOS because they didn't have as good of a handle on their main leads, there's no comparison between similar dramatic beats, and they didn't as effectively deliver the messages they were trying to convey.