Casuals get influenced by the word of mouth and online discourse, most fanboys and paid shills know that and that is why their activity peaks at certain points in the consoles’ lifespan trying to help generate positive or negative buzz, and the momentum generated in the launch window is a big influencer for casuals too.
The aura around Xbox One was weaker HW, predatory online policy, tiered launch strategy causing them unnecessary ill will in territories they were not prioritising (not what a global company should do), last two Xbox 360 years focused on casual games and Kinect and suffering for some first party AAA game draughts (not the case with PS3), big push for TVTVTV and Kinect in all boxes, as well as a slower console (which hurt their core branding slogan around performance “No power greater than x”), etc...
If Sony, after a decent launch in that scenario you described, managed to do a slim model for $349 or less, not impossible a year in if they wanted to, a $50 difference would not help Lockhart much if at all.