I'd honestly love to see Nintendo and Sony team up rather than compete. Nintendo can spearhead the handheld side, Sony could help Nintendo with consoles, which aside from about 3 years with the Wii have been a struggle since the SNES.
I'd like to be able to get Nintendo/Sony/3rd party content all on one console and ditto for one handheld. Perhaps even Sony/Nintendo branded smartphones that play games too. I'd ditch my Galaxy S4 in a heartbeat for that.