This is just a list of rivalries between Arrowverse/DC and Agents of S.H.I.E.L.D./MCU characters.
Kid Flash (Wally West) v Yo-yo (Elena Rodriguez)
Vibe (Cisco Ramon) v Quake (Daisy Johnson)
Harry Wells v Leopold Fitz *intelligence challenge*
Green Arrow (Oliver Queen) v Hawkeye (Clint Barton)
Killer Frost (Caitlin Snow) v Scarlet Witch (Wanda Maximoff)
A.T.O.M. (Ray Palmer) v Iron Man (Tony Stark)
Batman (Bruce Wayne) v Moon Knight (Mark Spector)
Amanda Waller v Nick Fury *intelligence battle*
A.R.G.U.S v S.H.I.E.L.D.
Lyla Michaels v Phil Coulson *who is the better director?*
Firestorm (Jax and Stein) v Thor
Supergirl (Kara Danvers) v Hulk (Bruce Banner)
Anti Monitor (Mobius) v Thanos
The Spectre (Oliver Queen) v The Ghost Rider (Robbie Reyes)
Final DC v Marvel Showdown: The Flash (Barry Allen) v Quicksilver (Pietro Maximoff)
Tell me who you think will win for each battle in the reviews.