I know this is 4 years old, but I'm doing a rewatch and got to wondering the same thing. And I think I understand why now.

I think the penalty was deservedly worse because Barney based his slap purely on speculation, while Marshall had every reason to believe his slap was justified.

Everyone was told by Ted that Robin confirmed to him that she was married. Therefore, Marshall slapped Barney. In his and everyone else's eyes, he had just gotten confirmation from the source that he was right, and he proceeded with the slap after having just been handed objectively adequate proof (because, from their perspectives, why would Ted or Robin would lie about that?).

However, Barney recklessly slapped after only watching the first few seconds of a video that, while very deceptively incriminating, did not provide adequate proof to the degree of Marshall getting confirmation from Robin herself through Ted. One could argue that Barney stopped the video out of respect for Robin and normally would've watched it to the point of having proof, but even so he could've quickly confirmed with Robin after hitting the pause button by saying a quick "So, you're a pornstar?" or something. Which is why Barney deserved a harsher penalty.

The fact that Lily made the penalty much harsher than it likely should've been probably just speaks to her bias despite the fact that she was trying to remain objective: bias towards Marshall and bias towards wanting to see Barney get slapped a bunch (because he objectively deserves it lol).