So I have to say it pleasantly surprised me. What was changed and what was kept for once made perfect sense, and it had the kind of innocence that a lot of modern cartoons have lost. Not just generic sweetness, but evidence that it was truly made to entertain young children, and not to lecture them or to wink at their bored parents.
My guess is that the biggest challenge with this kind of plot is explaining the relationship that sentient dogs, capable of romance and comprehending freedom, would have with the humans who keep them as pets. The original could afford to just gloss over it, since that's what we expect from animated classics, but the remake solves it by subtly building an alternate universe around the dogs. The setting looks historical but isn't, the dogs consider their owners as family but can also form families with other dogs, and everything is kind of charming and dreamy with no such thing as serious crime.
On the human level, the Aesop is that pets need to be loved and included even after a baby becomes the first priority. On the dog level, the Aesop is that you don't need to be the center of someone's world to be happy. I can't object to either of those and I doubt the original managed to lay it out so clearly for young minds. One thing I do remember about it is how incredibly confused I was as a child when Lady's neighbor dogs both offered to marry her. It's not that those themes are too adult, they're just too human. The new Tramp is less of a cad and there are no puppies at the end, so it looks like he's been responsibly neutered. Hey, that means a sequel wasn't set up, hooray!
You'll be happy to know that the weird Italian chef who decides to serve and serenade dogs in his back alley is not only present, but has a junior employee who is equally weird, and it's adorable.
So yeah even the music was pretty good. The "We Are Siamese" scene was admirably replaced with tabby cats and a catchy tune that I may actually have to look up so I can hear it again. (If you're wondering about my icon, my view on offensive stereotypes in old movies is basically that what's done is done. Enjoying the clever villain song from the 50s won't hurt anyone, but remaking the same song for a new movie would be unforgivable -- especially when all that's needed for the scene is a couple of evil kitties trashing a house for fun.)
And of course the doggos are precious. I hear Tramp was played by a rescue mutt, and he looks it, but he and all the others performed like pros, and the CGI backed them up just enough.
Don't expect this to be your new favorite Disney movie, but if you love dogs or if you've got a child to keep busy for a couple hours, go for it.