Weekends off in any 24/7 airline will be at the mercy of seniority. Total time off will tend to be a bit better in the 'legacy' carriers than the locos because of mature company/union working agreements. Time at home will tend to be more useful and longer on longhaul than shorthaul.
Shorthaul in any airline will rarely give you a nightstop of greater than mimimum length, and thus sightseeing opportunities will be severely limited. In longhaul it will depend on the schedule. many holiday-based routes aren't daily, and thus you may get two, three or more days at your destination. Depending on union agreements and flight time limitations, ultra-longhaul flights will normally have at least two local nights on the ground, so longhaul is the place to be if you want to see the world.
BA covers many more longhaul destinations than Virgin, who have only 25 or so destinations. However, individual fleets will not serve all destinations - I would guess that the BA 777 fleet has the widest coverage. Virgin has most of the best places to go, and few of the real fleapits of the world (depanding on your prefereneces), so the nice place/flight ratio is pretty good!
There are disadvantages, however, and they've been covered many times before. In short: fatigue, lack of poling time, extended stays away from home, and the impact of foreign food on a tender British digestive system are all reasons why longhaul doesn't suit everyone.