Contrary to the description of the feat both in-game and on wiki, the opponent, in fact, does get to perform a trip check against you. I've tested it and got knocked down multiple times after charging with a shield and hitting an opponent with it.If you hit an opponent with your shield as part of a charge action, in addition to dealing damage normally, you will perform a trip check without provoking an attack of opportunity. If you lose, the defender does not get to try to trip you in return.
In other words, not only does the feat not work as supposedly intended, it actually becomes a liability, too. Not exactly something you expect after investing two feats into getting that knockdown attempt.
https://wiki.bgtscc.net/index.php?title=Shield_Charge