Just to clear things up, I didn't mean try to get MR or Arnold to render out a scene that's a mix of shaders belonging to the respective renderers(as you found it, that doesn't work). I meant that you could set up render layers with shaders and settings specific to a particular render and batch them out, that's just one way. Or batch out separate scenes period. Either way you're compositing the elements into a final image in another program(After Effects, Nuke etc).

Given that the eye is modeled well , I'd say the material settings are only a part of it. In the case of the cornea, we already talked about Fresnel reflections and the correct IoR. We know it's almost completely transparent, highly reflective and smooth so that should be the starting point. Another aspect would be lighting and environment. That means not just having an environment for it to reflect but also proper exposure(it's near impossible to emulate photographs without taking this into consideration). If you break down the reference image a bit and check out "why", we'll figure out the "how". You'll see that the environment is high contrast with a large bright spot, that coupled with the child's dark eye color providing even more contrast makes the reflection really pop. The cityscape image is not similar to these conditions so you probably won't get comparable results even with Fresnel reflections. It looks kind of flat too(hopefully it's HDR).

Check this out, the reflection is prominent because the creator Chris Jones used a high contrast IBL with an isolated bright spot.

Eye Piece - YouTube

And just the eyeball. Alright I'm done ranting
Eyeball - YouTube