That's IF your animal control keeps track of tattoos. Mine doesn't. I sent in my dog's tattoo and microchip info. The confirmation I received has only his chip info on it. I guess their computer systems don't have fields for extra info like tattoos.
Do I like having my dog tattooed? Yes. It's a big obvious notice to anyone who thinks about stealing him that he's going to be easy to trace.
But also, as my vet and I once discussed, I've been going to them for 10 years and they like and trust me. If I brought in a new dog and told them I bought him, they'd never question it. Never ever in a million years. So what's to keep me from stealing a dog with a tattoo and passing him off as mine?
There'd be issues if I tried to register him with AKC, who has records of tattoos. But as long as I lay reasonably low, a tattoo isn't better "instead" of a chip.
Chips provide information if your dog gets lost. One phone call to the chip company and your phone number, address, alternative phone number (I have an out of area number in case of a local emergency), medical information (like, if your dog takes medicine) is provided to the person who has scanned your dog and calls (usually a vet or shelter).
I've found dogs that were chipped and tattoed. It was the chip that allowed me to return the dog home quickly and safely. I just brought them to a local vet. They made the phone call, and I brought the dog home -- in one case before the owner even realized that he was out wandering in traffic.
A tattoo doesn't do that.
For me, it's not either/or, but BOTH.