I think the influence was a high level of systems thinking. He didn't just design products, he designed what you could do with products, and he designed how and why people would want them - which is a level of insight that eludes anyone who thinks a product is a list of features or (worse) a technology stack.
Having said that, iMovie was good, iPhoto was okay-to-good, but iTunes has always been awful.
I've never understood why it was so badly designed. (And it's getting worse, by all accounts.)
iTunes is certainly awful to use, but the interesting part of that story is not iTunes itself, but the work and negotiation that had to happen to license music from all the major labels to populate the iTunes marketplace. Sony had a huge first-mover advantage in that space (their own global music label, movie studio, video game console AND the Walkman brand), but was too busy forcing its disparate businesses to compete against each other.
The end result being that they completely missed the boat on the then-nascent digital music market, and less than 15 years later, have spun off most of those brands and hardware-wise, Playstation aside, are limited to making (very nice) camera sensors for iPhones.
My favorite play was when he flew his private jet to the UK to bribe the man he stole the ipod design from to testify in court that he(Steve) did NOT steal the idea from Sony. Good stuff.
Having said that, iMovie was good, iPhoto was okay-to-good, but iTunes has always been awful.
I've never understood why it was so badly designed. (And it's getting worse, by all accounts.)