Raindrops and snow will not accumulate so easily on the black plastic cover. Furthermore any water or snow that resists falling off it will be away from the phase center of the horn and should degrade reception less than if it was just on front of the horn as with the membrane version. The black colour will also help the sun melt off any snow much faster.
Wet sticky snow that builds up on the feed of an offset dish is probably one of the major reasons for temporary bad reception up here in the north. The dishes are pointing very low here (elevation typically 13-20 deg for "normal" satellites) and so the LNB is pointing upwards.Easy to cure if the dish is low and easy to clean off but a pain if the dish is roof-mounted since the cause of the problem makes one very reluctant to go up and fix it.
I would pick the black-cover version anytime provided the cover doesn't introduce losses over the membrane.