I only know about cats, but Kai didn't change his tendency to roam, when he was neutered.
It did either stop him spraying in the house, or he managed to do it without being noticed, and once neutered it's a lot less smelly, so wasn't obvious. He did spray in the house twice before he was done, and it was hard work to remove the smell from the carpet.
As others have said, with cats, it's probably far more about population control, and I think it is likely Kai disappeared off to try and get his paw over with the local female cat population. Whenever he's around the house, he'll have a good sniff at Zev's rear, which may just be a general "hello" sniff, or may be him checking out whether she's ready for his attention!
Aside from their general abilities to escape and wander around the local area, I think cats are also somewhat more profligate breeders than dogs, so neutering/spaying is a far more necessary requirement.
I'm afraid that if I had a male dog, I suspect that I likely would have him neutered. Ultimately a pet dog isn't going to listen to us telling him he doesn't want to be a daddy, and even an accidental escape could result in some female dog finding herself pregnant, that would not otherwise happen. We do massively impact upon the life that a dog lives, it's hard to consider that this particular behaviour by us is worse than other things that we'll do. Allowed to roam the country, outside of our control, a dog may have a freer life, but it would also probably be much shorter, without access to modern veterinary care. Swings and roundabouts.