In Captain America: Civil War, during Tony's fight with Captain America at the Winter Soldier base in Siberia, Friday informs Tony that he cannot possibly beat Cap in hand-to-hand combat. Tony then asks Friday to analyze Cap's fighting style and provide him with countermeasures. In barely a minute or two, Friday has provided him with the information, and Tony quickly turns the tide of the fight. It's unclear if she's actually controlling his suit, or merely instructing him, but her information is vital to Tony's ability to stay in the fight.
Jarvis has shown the ability to locate weaknesses in enemy weapons systems, such as when he instructs Tony to target damaged components in Obadiah Stane's Iron Monger suit. He's also shown the ability to control Tony's Iron Man suits independently, and eliminate multiple targets with their weapons, as when he assisted Tony in fighting Aldrich Killian's Extremis brigade. However, I don't believe we've ever seen Jarvis do something as complex and urgent as Friday's countering of Cap's fighting style. From this, I conclude that Friday's capabilities - at least in terms of assisting Tony in operating his suits - are equal to or greater than Jarvis's. In areas other than combat, there may be other supporting (or contradictory) examples, but I found this an easy comparison that seems to line up directly.
It seems likely to me that Tony is always improving his AI assistants. Even if Friday was a lesser prototype or side project to begin with, after using Friday for a few months, Tony could possibly bring her up to the level of capability that Jarvis previously had. From her performance in Civil War, I think we see that this is the case.