I'll be honest, I've only ever done Champions char gen.
IME, 99% of the headaches of HERO are in CharGen or improvement. When you sit down to actually play, you might never even touch the book because virtually everything you need except the Speed chard is on your character sheet.Well, that'll color your view, but even there its not complicated if you don't make it so. In most incarnations of the game I could put together a flying energy projector or a brick in ten minutes.
Which doesn't mean it can't turn into a fairly complicated process if you have a fairly specific result you're aiming at with powers, because it absolutely can. That's absolutely the price of powers that are able to be heavily fine tuned, and if that doesn't matter to you, it can seem overly fiddly.
The worst I can say about it when powers are not involved is its a game of its time which means the skills are split finer than probably a lot of people care about, but outside that, you buy attributes (and that's a fair bit more straightforward with the current edition), buy skills, maybe buy a couple talents or perks, and you're done.
(Of course some people will compare it to generating things like a first level D&D character, but it should be noted even a heroic scale Hero character is more comparable to, say, a 4th level D&D character (and may be more like an 8th level one depending on set up) so there's a certain lack of comparing apples to apples going on).
And the headaches occur because of a combination of the math- not really complicated, just lots of it- and the open nature of the game. There’s almost no One Way to do any kind of character, there’s dozens. There’s simple and straightforward ways and arcanely complicated and intricate ways of building any character you can think of.