At first only a couple days before I didn't think it was likely the Switch would outsell it because the Nintendo systems usually don't have long legs compared to Playstation consoles. However, after seeing this recent quarter and realizing how the Switch has the potential to sell 30M in this fiscal year alone and its been growing YoY entering its fourth year, its showing me that the Switch is gonna sell for a long time because even if sales drop next year, its gonna take a while for the Switch to completely die off in sales. For example, let's say the Switch sells a conservative 25 Million this fiscal year, the Switch would be at 81M by March 2020 and lets say after this fiscal year the Switch starts slowing down exactly like the Wii did after selling 25M. If the Switch slowed down the exact way the Wii did(Which By many is believed to fall off a cliff) The Switch would end up selling 132M units, which definitely could put it above PS4 numbers. And that's ASSUMING the Switch slows down exactly like the Wii did, which seems less likely to happen to the Switch since the Switch will continuously get software support from both handheld and console divisions, multiple revisions are likely coming to increase sales, and Switch is essentially a handheld where we're more likely to see one portable device per person rather than per household. Also, unlike the Wii's main gimmick of motion controls that got boring quick, the Switch's main gimmick of being a hybrid home/portable console is timeless and will always be appealing. So its seems like the Switch will have an even LARGER lifespan than the Wii, which would likely put the Switch's total over 132 Million.
So as a result, I think the Switch will outsell the PS4