I think it makes sense to follow the UI guidelines recommended by the vendor (Apple and Google) for their respective device for the following reasons.
People know what they are signing up for when they buy either of these devices. It's not like they walk into the store and say "Give me the best smartphone there is". They've likely already made up their mind before they go to the store.
So you can assume the user to expect the OS styles to follow a certain pattern that uniquely differentiates it from the rest. Android has the flat icons style, iOS is all about gradients, Windows Phone is all about tiles, etc.
So it would be a little disappointing to the user if the app maker decides to shove one specific vendor style down the throat of all the users across different platforms and devices. The user might be thinking "Why am I seeing iOS style buttons and titlebars on my Android phone? If I wanted an iPhone, I would have gotten an iPhone. Why does this app creator think everyone is on an iPhone?"
See my point?
Another thing is that people might think the app creator is just being lazy by coming up with a "one design fits all" approach.
If you think by having a similar UI across all platforms, you are being consistent, then you need to rethink what consistency means in this specific context. What type of users are you talking about that is looking for this "consistency"? Are you worried about users that are switching phones (iPhone to Android or vice versa) and want them to have a consistent experience? It's very unlikely that such users will complain because as I said earlier, they know what they're signing up for when they buy a phone.
The only reason I can think of when you may want the same UI on every platform is if you are building games like Angry Birds, Cut the rope, etc.
Hope that helps.