Having the most powerful hardware is bigger factor for your enthusiast gaming crowd. I would suspect that the majority of PS4 Pro and Xbox One X purchases were to be people who already purchased a base console, and are willing to upgrade. So with that in mind, it makes sense that early adopters will place a greater emphasis on power when deciding which new console to purchase. As you get beyond those early adopters, the importance of power is less and less relevant. For for the first 18 months on the market, its power is a factor that carries some weight.
With that said, marketing/branding/messaging are big factors. Sony rolled out the PS4 with excellent messaging from day one. Their commercials during the launch window were excellent. The launch lineup of software was mostly loaded with a bunch of cross gen titles, nothing that really stood out as system sellers, but the PS4 got off to a terrific start anyway.
Nintendo is probably the only manufacture where their exclusive software is a huge factor in the success of the platform. For the PlayStation and Xbox, its relevant, but the majority of the most popular games on those platforms are multi platform. I do believe Sonys exclusives help the PS4 separate itself from the Xbox One, and it is a significant factor in why the PS4 has sold over twice as many units as the Xbox One.
People like to write off the Wii, but it is in fact a videogame console that sold the most units. It wont that generation. Just because it was unique is no reason to write it off. Yes, a lot of casuals bought one and did not stick with gaming beyond the Wii, but many others were certainly gamers, and I would suspect that many 360/PS3 gamers also owned a Wii. Games like Mario Galaxy 1 & 2, and Zelda TP, Metroid Prime 3 and Donkey Kong Country Returns didnt sell well because of grandmas who owned a Wii, there were plenty traditional gaming experiences on the Wii. Nintendo has done a good job of offering products that appeal to a lot of people, and owning a PlayStation or Xbox doesn't make Nintendo's platform any less appealing. If you own a PS4, and Gears of War and Halo arent that important to you, then owning an Xbox One would be pretty redundant. You couldnt say that with the Wii, and you wouldnt say it now with the Switch.