I'd probably go for the lunch.
Biggest reasons are logistical and timing, which may or may not apply to you.
I don't rent a car, so getting from another resort to Animal Kingdom Lodge for breakfast is a bit of a challenge. Basically, you have to bus to a park (like Animal Kingdom) and then take the bus there to AKL. If you have a car, that's not really a huge decision making concern. If you're staying at AKL, I'd do an earlier breakfast at Boma so you can get going to a park.
But if you're enjoying Animal Kingdom at rope drop (or near) you're going to have to leave to go to your late breakfast. Not a really something I'm usually interested in doing. If you're not 'up and at em' people, then this may not be a huge concern, if you're not interested in touring AK first thing in the morning.
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