Library is a factor in people's purchasing decision. And an important one for sure. It is not the only factor and the relative importance of each of these factors is going to be different from person to person. It is very hard to evaluate how a group as diverse console-buyers are going to weigh these factors without projecting one's own thought processes onto them. The level of certainty you have on what is proven and known without the support of comprehensive market research to back it up is unwarranted.
I didn't know an opinion required comprehensive market research to back it up.
My level of certainty I have is from following the gaming market closely for the past 15 years. That's enough data for me to be pretty certain of my opinion. But maybe I can at least expand on why I think that exclusives matter more than raw power.
The most powerful console hasn't always been the best selling console, that's a fact.
As far as XB vs PS, XB has generally had more raw power, or has been the more capable console, and also generally cheaper as well; yet PS has sold extremely well internationally, and XB struggles outside of the US/UK. Why do
you think that is? What else would make people view PS as a better purchase than XB?
Again, PS has 2 of the top 3 best selling consoles of all time... that's also a fact. PS4 will no doubt pass the PS1 and Wii and PS will hold the top 3 spots.
So why has PS been so successful? What are they known for? They weren't always the most powerful console. They weren't always the cheapest console. But what have they consistently done for all of their consoles, which includes the PS3? They were able to provide a strong 1P software lineup to compliment their strong 3P software lineup, giving them the largest and most diverse software lineup of any other company. They make games that appeal to many different gamers.
The only reason the PS3 sold poorly compared to other PS systems is because Sony, quite frankly, fucked up. They were arrogant and made a complicated HW design, priced it too high and expected everyone to be loyal to their brand. Despite this, they still went on to sell ~85M, which is by no means bad in its own right.
Preferences aside, it's a well known fact that Sony's 1P output has been one of the best in the business, arguably as good as Nintendo's. What separates Sony from Nintendo is 3P support, where Sony is clearly on top. Nintendo's strong 1P output is the biggest reason why people buy Nintendo systems... they provide very good exclusive gaming experiences not available on any other platform. They too sell well internationally. Coincidence?
Furthermore, when it comes to XB/PS anyway, I think the majority of early HW sales are from core gamers, ie the people who give a damn about graphics. Once they saturate the core market, they usually need to reduce the price to get the casual gamers to bite. Once consoles receive price cuts, or specifically reach the sub $300 or $200 marks, that's when sales start to pick up. That's why I feel that the casual gamers make up for a larger portion of sales than core gamers. And I honestly feel that casual gamers care less about graphics and more about games.
Tl;dr, that's why I feel that brand presence is the most important factor, followed by price, then power. You need high quality exclusive gaming experiences or a diverse software library to appeal to many gamers internationally and choose your system over the competition. You need your console to be priced low enough to reach out to casual gamers. You need decent hardware to make your system appealing to core gamers. The latter two are kind of a balancing act. I feel like Sony have done an excellent job of balancing all 3 with the PS1, PS2 and PS4. PS3 they failed on pricing.
I feel that Nintendo has generally been good at achieving 1 and 2, while MS has generally been good at achieving 2 and 3.