At actually grappling opponents they indeed compete very well with barbarians. At staying alive after restricting an enemy to close range (the “secret” requirement for any grappler), they fall decidedly behind barbarians (and even grappler rogues thanks to their uncanny dodge and evasion, or grappler wizards thanks to arcane ward+shield).
At mobility (a nice boost for grapplers but not strictly necessary) they again fall behind the barbarian and rogue thanks to increased movement speed and cunning actions, but are about on par with the wizard.
At the end of the day, if I want a grappler, there are at least three other classes I’d choose first now that the prodigy feat makes expertise available to all.