I think it varies by market. NA has shown virtually no "loyalty" dating back to the days of Atari, always going with whatever they (or "we" rather, as I've done this myself) deem the best deal. If the next Playstation is priced higher than Microsoft's offering they will inevitably lose some of their share of the market here.
In a place like Europe or Japan, though, I'm not sure it would have too big of an impact. Those two regions just don't seem particularly fond of the Xbox brand regardless of circumstance.
I'm curious about whether or not the Switch would cut into the sales of the other two... It has long seemed like whereas Sony and Microsoft's sales directly eat away at the other's, Nintendo doesn't seem particularly affected by this competition.