We caught a bunch of toads on the roads when I was a kid for a frog jumping contest, and put them in our yard when it was over. We've had toads in the neighborhood ever since.
They poop around the yard (mostly on the sidewalks), and by examining it, I can tell they eat a lot of pill bugs (which we also have in abundance). I believe they'll eat ladybugs, too, if they're on the ground (fortunately, they're usually higher up).
Our toads (which make a call that sounds like that of Woodhouse's toads, or Anaxyrus woodhousii, and look similar to those, but may be a hybrid species) somehow like to make burrows in our very compact soil. They live in holes under concrete blocks, under the ground by the holes in our black plastic (where we plant vegetables), under the ground generally (I've dug them up on accident), and stuff like that. They love to be warm, and when we had insulation out on the patio, we would find toads sleeping under it every morning.
Back in the 1980's when we used a Bug Zapper, they would sit under the Bug Zapper and eat the critters it attracted.
They somehow breed, although I don't know quite how, since the closest body of water is a ways away and down a steep cliff, and we still see tiny toads appear in our yard with regularity (and I live in a semi-arid climate; my guess is they somehow have tadpoles under ground that mature into toads there).
I can't say whether the toads make a big difference in the insect population, but they're fun to have around. Kids love them (but make sure they're nice to them). They look like rocks at night, though, and they blend in with the cement/concrete and dirt paths; so, be careful not to step on them. If we're watching them, they usually stay still (seeming to pretend to be rocks) until we go away (so they're easy to catch, and they may not jump to get out of your way if you're walking; so, don't assume they will).
Our toads are active and feed at night. They sleep during the day.
We've had a bullfrog before, too, in an artificial black plastic pond (from a tadpole we caught). Bullfrogs require a lot of water, and wouldn't be practical for removing pests from your garden. They would probably die from drought in most gardens. Toads seem to be much more accustomed to living near humans.
Unlike our toads, bullfrogs are easily startled and will do their best to get away from you at the slightest provocation. They're fast.
As much as we've had a lot of toads, I wouldn't say they were ever out of control.
If you somehow upset the toads by accidentally fertilizing them (when their hole is under your plants), they may run away and not come back for a year or two.