Well, we recently <a few months ago> moved from a small condo to a much bigger house, with a yard and a back-house and everything. We did hire movers for the big stuff, because we were only moving a few blocks away and it was easy to just move a lot of the small stuff with car or pickup.
Then we hit the storage shed, tossed some stuff, brought out most of the stuff…
And…now we’re downsizing to just about nothing. I am right this minute throwing out as much as I can bear. Got a HUGE pile of stuff for Goodwill to come pick up, and it will get much bigger as we go on. We have at least two dump runs scheduled for later, and hubby is trying to sell what he can on Craigslist. (Lack of work in the area = separating for a while, to different states, while I try to pick up work elsewhere. So it’s temporary, until we get money together, bills paid off, and decide where to live, but for right now, and for quite a while, it’s going to suuuuuuuuuuck>
Right now all that’s going into storage will be the appliances <still haven’t even paid them off /facepalm> and stuff too personal to toss out.
I’d say movers are worth it for the big stuff, and if you have to hire them for any length of time, then you might as well let them take boxes of things you’ve packed up, too. We only had to hire them for a couple of hours, and the space that was leftover was goofy; we could have had them move a lot more 
We do have pets, and the cats are already glaring at me 'cause they remember what all the ‘boxes’ meant last time and they aren’t too happy. We just chose one room to close them off in, in the new place, and if you can, bring as much of ‘their stuff’ as you can into that room ahead of time. Then bring them over <ours cried the whole way; first time they’d been in a car since they were a few months old and got fixed> and put them in the room until the movers have done their thing. If it’s cats, and there’s a window, maybe put something in there they can sit on so they can see out it, and see what’s going on. If it’s dogs, then just go in there as often as you can to reassure them, or let them out into the rest of the house if you’re not worried about their escaping out the door.