Actually after the Spring of 1863, the Federal Cavalry in the Army of the Potomac handled itself pretty well. It bloodied Stuart’s cavalry at Brandy Station and beat them at Gettysburg on July 3, 1863. Stuart paid with his life fighting the “inept” Federal cavalry at Yellow Tavern in 1864. And it was Federal Cavalry that contributed greatly to the failure of Lee’s Army to escape from Appomattox C.H. in 1865.
Early in the War, the Federal cavalry was hampered by command which didn’t utilize them very effectively and often relegated them to the status of simple scouts and vedettes. By Gettysburg, a generation of younger officers were at the reins (pun intended) who were much more willing to use the Federal cavalry as a mobile fighting force.
The Federal cavalry almost always had the advantage in weaponry (small arms and horse artillery) and in the quality and quantity of mounts (the Giesboro Point Depot alone trained, readied and rehabilitated thousands of cavalry mounts for Federal service).
I would put it this way,
Infantry - even
Cavalry - edge to the South
Artillery - overwhelming Federal advantage