Generally I think you should share things and costs and we generally do, but my partner is far better off financially than I am and we had a conversation about this because he was very aware that that approach all the time would limit were we went and what we did because I would be broke very quickly and put under stress to 'keep up', so now I pay my share if we're doing normal stuff and extra special things he pays for. He's big on presents and surprises as well but that's just a personality thing, he enjoys it, and sometimes they are expensive and sometimes they cost absolutely nothing, and in turn I surprise him as well.
It's not about the cost it's about the equality of thought and care, but I'd never 'expect' him to pay for things just because he's the man, that's just rude and also somewhat lacking self-respect and equally a wealthy man shouldn't use money as a cop out to buy presents in lieu of genuine care and attention because that means nothing.