Having done a fair amount of BLE work with Android, iOS, and Windows development, I'll say that transferring large amounts of data is a pain.
The real limitations come from the iOS side actually, because they internally limit the transfer latencies (this has improved from iOS 6 to iOS 7, and I haven't tested throughput on iOS 8 yet).
Bluegiga has some old performance testing data here: https://bluegiga.zendesk.com/entries/22400867--HOW-TO-Maximize-throughput-with-BLE-modules
My personal testing (BLE112 and iOS 6 or 7) showed about 1000 bytes/s using acknowledged data transfer, and 4000 bytes/second with unacknowledged data transfer. I don't think this was an optimal testing condition, but it gives a good ballpark.
From Bluegiga (ideal conditions):
The best we have seen between two of our BLE modules is about 60Kbps
(unacknowledged packets).
The future of BLE looks good, as BT 4.2 is pushing a bit on the throughput (via increasing packet sizes): https://en.wikipedia.org/wiki/Bluetooth#Bluetooth_v4.2
Unfortunately, the silicon for that probably won't come out until later this year, and who knows when it'll be supported by iOS (and Android).