The pump gun will always be more mechanically reliable. There's less to break down. However, pump gun problems are more due to operator error than a parts breakdown. Under the right circumstances, a short stroked 870 resulting a double feed will put the gun out of commission and there is no quick fix.
Semi autos require more maintenance but are less dependent on the operator. Reliability problems usually stem from poor cleaning or weak ammunition. In these events, the gun becomes a manually operated repeater and will still function. However, if the rear linkages break then your semi is out of business until the parts can be replaced.
I've used and owned both types of guns. For pure simplicity, I prefer my 870 but I've used them for years and have confidence in my ability even under pressure. But I also think that with ammo of suitable power, a well-maintained Benelli, in the hands of a less experienced operator, will be more reliable in practical terms than the pump.
Paul