Shredder had crazy ninja skills and beat up the turtles in ways I don't think Cap could do. He was also a robot controlled by krang so he doesn't have normal human stats so it closes the gap usual non super powered guys have when fighting any Captain America. Shredder seems capable with all types of weapons so he might be able to take, use or make sure the shield is BFR to make it more in his favor.
The legendary, original Shredder was a Tengu Demon named Oroku Saki, or "Tengu Shredder". Ch'rell the Krang/Utrom criminal stole an exosuit when the Utrom crashed in Feudal Japan and based his Shredder design and the Foot Clan off of the demon.
So the first Shredder was a demon, the next was a robot. Karai was the only human Shredder from the TMNT series.
For clarification it's Krang robo-Shredder. I would think the tengu version of shredder wouldn't have much showings to give a clear cut winner in any fight.
Tengu demon was gonna conquer Japan if left unchecked. Oroku Saki Shredder(human/demon hybrid) was gonna conquer the world and it took 4 of the strongest fighters from Japan training until they gained super powers to fight him.