Their first post-Crisis fight (written by Billy's solo series author, Jerry Ordway) certainly showed that Billy could give as good as he got against Adam. And as you can probably tell from the dialogue, Billy was new to his powers in that story. Adam was eventually defeated when Billy removed his Scarab necklace, depowering him.

https://imgur.com/a/4xBwf


In their next fight, early in Billy's solo series, Adam was able to dominate Billy, who was at one third of full power, since he was power-sharing with Mary and Freddy at the time. Billy received a broken arm, and would have died, if Mary and Freddy hadn't powered down just in time for him save himself from being drowned in wet cement.

https://imgur.com/a/jTe7T


A few issues later, Adam once again fights a power-sharing Billy, who still has his broken arm in a cast and sling. A punch from Billy sends Adam flying though, because by this point, Ibis had assumed the responsibility of keeping the Seven Deadly Sins imprisoned from the wizard Shazam, which freed up more of the wizard's power to be used by the Marvels. As far as I can tell, this was a permanent power-up for Billy, which makes his first showing against Adam all the more impressive.

https://imgur.com/a/uzBNq


They had one more fight near the end of Billy's series, an even one with no winner.

https://imgur.com/a/vInqr