My son's issue is different and he seems to do fine on variousdevices. But I have some remaining strabismus along with permanent effects of amblyopia. I find phone screens and Nintendo DS type devices very fatiguing. I know in general even on a computer, I need to look up relatively frequently and make sure my eyes are roving. Many games seem to lead to a more intense focus with less thought to looking away. I don't have similar fatigue issues using the new iPad as as I do with smaller screen devices but in general I find the larger the screen the better off I am overall. The iPad also has free access to apps we've had for the iPhone.
