To me "Progressive" means rhythmically and dynamically so. Not just 17/9 time or whatnot, but maybe Flamenco influenced or Jazz, New Orleans flavor to the metal or something, and different layers, different moods throughout vs steady blast beats, or thrash.
Maiden is pretty progressive for their time with mythologically themed, epic songs influenced by Classical and Opera.
Is that "deeper," well, yes. It's deeper in the way a great novel (Rhyme of the Ancient Mariner) is deeper than a murder mystery. nothing wrong with a good murder mystery, but it's different. There's 100,000 murder mysteries, all basically the same. Some are better than others, but its genre fiction. Maiden weren't doing that. They were trying, at least, to do something more ambitious and, if you want, deeper.
Opeth were doing that, too.