To reproduce:
1) Open attached project and scene in it
2) Make sure GPU Skinning in Player Settings is enabled
3) Build and run on Android
4) Switch between different models with buttons - notice that FPS is significantly lower when Skinned Mesh Renderer is used
5) Go back to editor
6) Disable GPU Skinning
7) Rebuild the app
8) Notice that FPS is equal over all devices no matter which models were used

DUT:
Samsung Galaxy S4 mini (Adreno 305) (Android 4.4.2) (35 FPS skinned vs 60 FPS normal)
Samsung Galaxy Note 10.1 2014 WiFi (ARM Mali-T628MP6) (Android 4.4.2) (30 FPS skinned vs 40 FPS normal)
Samsung Galaxy S5 Neo (ARM Mali-T720) (Android 5.1.1) (35 FPS skinned vs 40 FPS normal)
Motorola Moto G (Adreno 305) (Android 5.1) (35 FPS no matter the models - no repro)
Samsung Galaxy S4 (GT-i9505) (Adreno 320) (Android 4.2.2) (60 FPS no matter the models - no repro)

RESOLUTION: Not reproducible, GPU skinning has been disabled on Mobile platforms due to unpredictable performance. The primary reason for this is that we need to read GPU skinning results from the CPU, this introduces a dependency that certain device drivers don't like at all.