I see the following advantages of the Otii over the BattLab.
1) Otii is able to measure, log and give a real time display of the current over long periods of time. The current graph display is active visible real time which is a major advantage when debugging to get peripherals to go into low power. The long capture periods can do long term averaging of the different active and sleep and different current, power, and energy levels of these. The BattLab does its capture over a fixed time period and then displays, which works for many use cases but is nowhere near as powerful. It may be possible to fix this with new firmware and application but I am not seeing much activity to develop new releases.
2) The user interface of Otii is much better especially for debugging and testing. This I think could be improved if the user interface of the BattLAb put the battery analysis stuff in a separate menu and concentrated the main page to more general data collection.
3) The Otii has a much more flexible and configurable analogue front end. I have been able to use the additional current and voltage measurement channels to completely measure the performance of a solar powered wireless device with a small LiPo battery for our balloon tracker. It was possible to see the charging and discharging processes as separate traces on the graph. Not something I use often but of massive value when I did.
4) Otii is auto ranging between its 3 current ranges so easy to measure, log and display a wide range of current scenarios in one capture.
Thus I agree with Jeremy that the Otii is much better. The choice depends on our budget and what value members put on such a device. The BattLab gives a lot for the money and is Open Hardware and Software. I did previously use the Nordic Power Profiler (PPK) but that had a current maximum of 70mA which was too low for most embedded WiFi and complex sensor devices.
I do think either Otii or BattLab would be a good addition to our rLab test bench for low power embedded devices. I use mine more than my oscilloscope but not as much as my Segger and multi-meter.
Richard