can't speak for the 737, but the Airbus is not that bad. for the first six months or so, you can expect 'blind lines'. In other words you get the trips that no one has bid for. This can be good, it can be bad, just depends on luck. Once your seniority increases, you get more control over your roster.
A collegue of mine had 3 weekends off in 1 month on a blind line last month...and he is quite junior. I on the other hand worked them all!!!