characters must make a strength attack to initiate the Grab, but the Grabbed target gets to use a skill (and the accordingly higher modifier) to escape!
There is only a bonus to escape if the grabbed target is trained in the skill they are trying to use to escape. Otherwise, the grab and the escape should have about the same bonus, stat plus half level vs Reflex or Fortitude. Most monsters are not trained in Athletics or Acrobatics. PC's have the slight upper hand escaping a grab at low levels, though at high levels that upper hand slowly diminishes.