A lot depends on what the parents were bred for and how well the cross was chosen. A good solid minded Arabian with proper gaits and conformation crossed with a well bred and solid conformation quarter horse will give you an excellent cross. Though you cannot predict if they will inherit more from sire or dam or be somewhere in between, it will be a good cross. My mom bred some beautiful Arabian mares to the same quarter horse stud. She got 2 fillies the first year and 2 colts the second year. Each matured to different heights, builds, and overall appearance. One of the mare's offspring had a very moody, aggressive daughter and a son with a very gentle disposition that grew very tall and was so lazy that nothing bothered him. The other mare's offspring had a short, stocky WP built daughter and a sleeker, high energy English built son. All were well put together with solid conformation, but were suited to different disciplines and rider ability.
Just like any breed or popular cross breeds, they are varied in natural abilities and dispositions. Judge each individually and not lumped together in a mass that does not hold true for each one.