Hum. I think if most of the intended audience of 'Sucker Punch' watched 'Birds of Prey', they'd be really disappointed. The former is wank fodder for teens with a really dark plot and lots of mindless action. I can't think of any similarities between the two save maybe one: I think a point you're trying to make here is 'Birds of Prey is style over substance', which I would probably agree with.
they both rely heavily on meta-style.
Look at SP for example; Babydoll, the protagonist, she'named Babydoll, looks like a baby doll, has the dripping submissive sexyness that most incels dream of, but, she's also a badass, WITH A KATANA. And has 2 companions who also are built out of picking all the baddest bestest traits you can find on social media. Nobody is down to earth here, everyone is the epitome of a completely synthetic character.
You can draw parallels with characters such as General Grevious (lol). First, he's actually named "grevious". He's a robot, because that's badass. He's got an evil looking face because obviously that's badass, and he's got four arms, and not only does he wield four lightsabers, but his arms can windmill - making him and unstoppable whirlwind of death! (oh and he's got a cloak too).
How much more can you throw in every exaggerated characteristic you can think of. WHy not have body spikes, a prehensile tail made of razorblades, no, ELECTRIFIED razorblades, A GUN THAT SHOOTS GUNS.
SP is in a way more subdued in the amount of shit it throws at the screen. After having the protagonist teleported in an ancient arena to fight a gigantic samurai, it doesn't really need any more than that, and it gives us time to absorb all the various meta that scene contains. I would still argue that it's too much meta, but BOP (or rather, BoP:&TFEO1HQ) has waaaaaaaaaaay more than that. It's style change after style change after style change after style change and 3 seconds cameos and cutaways and multimedia compositions and everything else that's the personification of ADHD. They probably described this film as a rollercoaster of emotions, but, can we really follow along for the ride? Was this film meant for humans?
You like The Fifth Element, right?
You know that scene where they introduce Ruby Rhod?
this scene is meant as a comic relief interval in the otherwise straight (if not too straight) action scifi of the rest of teh film. Sure, the characters are a bit over the top, but essentially it's Steve Dallas the straight hero must help damsel in distress Lelo get to the mcguffin to save the world from impending doom. Evil police forces try to stop them, so they must evade them, and then final confrontation with EvilGuy(tm).
Imagine you take this scene, compress it a bit, and, that's ONE scene from your film. And then you proceed to have every next scene be just as weird, over-costumed, over-produced, visual bullshit.
In BOP, the egg sandwich scene is pretty darn good, if it has been made a bit more realistic, a bit more human, we could maybe appreciate it more. Quirky filmmaking technique is meant to punctuate a film, not be everything that film's made of, which is what BOP is. It's a collage of weird filmmaking techniques and overproduced scenes, specifically designed for the ADD crowd who want to blitz their prefrontal lobe on echo chamber meta.
It's like watching pron on six screens while on coke.