I grew up with a Benjamin .177 similar to the one in the OP. I inlaid a patch box/nipple box into the stock, kinda like on the old Kentucky rifles, so I can keep a good supply of pellets right with the gun. I also have a scope mount for it, and used it back when I'd spend the afternoon shooting birds out in the cow lot to 80 yards. Of course I missed way more than I hit at that range; it's about like shooting an old buffalo gun at 800 yards.
For my uses, I greatly prefer a gun that you can pump up like this. I used it for shooting sparrows & cowbirds in the barns and sheds all the time, and this way I could put just a couple pumps in it so I didn't put holes in the roof. If I wanted full power all the time, I'd just use a .22.
Mine used to be pretty accurate (I think the rifling has been buggered up by shooting darts with it in college); I could keep shots in a half dollar sized group offhand at 35 yards. But the pellets were obviously running out of steam at that range. If ya hit a grackle in the wing at that distance, more often than not it would just knock a bunch of his big wing feathers out, and he'd fly away unharmed. At longer ranges the bird had to be facing me directly so I could put it in a spot that wasn't armored.
I have read reports from many people over the years who are enthusiastic about going after bigger critters with airguns in this class, but I'm not one of them- had plenty of bad experiences in that regard, and almost no good ones. If I need to shoot anything bigger than a gray squirrel, I reach for a real firearm.