Any phone that requires a case is going to be bulkier than one that doesn't so this automatically means that the iPhone will be bulkier in the pocket than his budget Android.
If you go the budget phone route you'll probably buy a new phone more often because why not. They're cheap. If next year's model is a decent upgrade you'll probably get it.
I run into people with iPhones that look like they've been through hell despite the case, glass cracked in three places, edges scuffed, outdated model... because frankly they can't afford a new phone all the time so they have to live with this one. But they'll say they just HAVE to have an iPhone and would never consider Android.
Personally I'm somewhere in the middle of the two extremes with a Samsung A5 that costs a couple hundred bucks. Maybe I should ditch the case.