I'm talking about Breeze and DevForce. DevForce 2012 supports Windows 8 tablets for example, but yes for non-.NET clients we are talking Breeze. Both follow the same model. Mobile websites suffer from the same issues that they have to go back to the server for every page.
As far as exposing business logic to the outside world goes, if the client technology is different from the server technology you have no other option than implementing the logic twice. For example in case of Breeze with a .NET back-end.
Where the client technology is the same as with DevForce you can architect things such that you can share the business logic. The way to accomplish this is by separating the loading/saving from the actual logic that operates on the data in cache.
Unfortunately, the answer to this question comes down to who you decide should suffer. The developers having to implement and test the logic multiple times or the end-user with slow application performance. I personally side with the end-user. The end-user should have the best user experience possible and the developers should pay the price to implement it. That's how Apple became successful with all their iDevices.