I'm referencing only as in-games and not the overall lore on this matter.

From what has occurred in TESO, to me it seems Molag Bal is the most powerful and/or influential Daedric Prince we have seen throughout all the games released in the TES series. The only other Daedric Princes that would come close are Mehrunes Dagon, who has attempted and nearly succeeded invading Tamriel in two games (Battlespire and Oblivion) and maybe Sheogorath from Oblivion. Otherwise, it seems the other Princes have pretty much been pretty laid back throughout the games with the only Prince coming to mind being Clavicus Vile in Redguard playing a somewhat nuisance. But Molag Bal has managed to really cause massive problems on a continental scale in TESO that trumps even Dagon. Anyone else agree with this?

While we're on the subject, what Daedric Prince do you think has been the most powerful/influential lore-wise (in and out of games)?

It's all a ruse. Bal's ego is still hurt from the Dawn era, when Jyggalag use to dominate Coldharbour, and the rest of Oblivion.

As Hevnoraak said above, Jyggalag is outright said to be the most powerful Prince.

In addition, there's a few others that I would add as "most influential":

Boet-hiah gave us the Chimer, eventually leading to that bit of pleasantness with Lorkhan's blood-mover.

Meridia gave support to Umaril, who was apparently enough of a threat that an avatar of Talos himself had to intervene to give guidance to the mantled Pelin-el to defeat him. Ultimately, it took one of TES' biggest badasses to put Umaril down.

I'd also give Dagon a little more credit; his forces destroyed Ald'ruhn and Crystal Tower and ended the Dragonborn dynasty, hastening the Tribunal's end and giving the Thalmor an opportunity to rise. By proxy, Sheogorath-as-CoC would be equally influential, being a major player in Dagon's defeat (assuming you RP'd that way).