Which puncture-resistant tires?
The Schwalbe Marathon Plus (not just the Marathon) is widely regarded as the most flat-proof tire out there. It's also heavy and expensive, but if your priority is avoiding punctures, I don't think it can be beaten. ISTR reading about a round-the-world rider completing 50,000 miles on a pair without a flat.

Specialized Armadillos are not, in my experience, particularly flat-resistant, although there might be a beefier version than the one I was riding on. I have no experience with the Gatorskins.

Anyhow, there are definitely differences between flat-resistant tires. There are even differences between Schwalbe Marathons variants.