Happychick I disagree
I don't think boys do aspire to be Henry as he's always in trouble,most of the time is outwitted and has to live with an annoyingly perfect brother who can do no wrong. Neither of my twin boys(6 nearly 7) want to be him they just marvel at his audacity and the clever touches in the books. They feel sorry for him.
The issues aren't just siblings,peers and parents and the solutions aren't always cheating,bullying or pushing people about.
Sometimes HH is the one being bullied.
In the tooth fairy one HH is desperate for a tooth to fall out(as is one of my twins),he tries everything,uses his innitiative to come up with some clever ideas eg the sweets,plastic fang etc. The letter saying "nice try Henry" at the end had us all in stitches and HH got his come uppance.
In the Demon Dinnerlady the dinnerlady was bullying all the kids and stealing their food.HH came up with the idea of putting hot mustard in his food-problem solved. Incidentally Mirander Richardson as a cockney dinner lady is as I said before pure genius.
In HH Goes to Work Bill is bullying HH so he comes up with the photocopier plan.
There are stories about things like weddings,boring campsites,nits,living with a perfect sibling,injections etc. Things kids (or should I say boys)often feel but never get to articulate. Kids love to marvel at how Henry overcomes said issues.
Both Horrid Henry and Perfect Peter are over characterized and I think most kids can see that,my two certainly do. Nobody likes a perfect Peter or a horrid Henry.
Most of the time Henry gets his come uppance and punished and a moral is a big part of the story.I actually think the books are good at illustrating to kids what will happen if you live out your fantasy and behave badly.
There are stories where he does get away with it but he often doesn't and the author is clever at slipping in what most kids know will/should be coming eg the muddy pyjamas in the fairy story, the plastic coin in the Tooth Fairy,the doctor's injection in the injection one.
I think this is what gets them reading the books, the will he/won't he get away with it this time,often just when you think he will he's thwarted at the very,very end.