The Wii captured a fundamentally different market from its competition: that was the whole "blue ocean" strategy Nintendo had in mind, building on success with the DS. The 360 and PS3 sold "convergence" devices instead: they did a little bit of everything home-entertainment related. Enthusiasts with the cash to spare would end up with multiple consoles for the exclusives, but in that generation the software barriers to exclusivity were starting to come down; the PS3 had a more unfamiliar architecture than the 360, but regardless, cross-platform releases running the same engine and assets, vs a completely recoded game with different assets, were now becoming the norm across both consoles, so it was not like the old days of Sega vs Nintendo where you could have a totally different view of gaming by getting one or the other; the high end was actually getting a bit commoditized, and it was just the first-party exclusives that added differentiation.
But the broader market was in unexpected places like senior centers, where Nintendo's offering found an ultra-casual niche. For those markets, it never had to do anything more than play Wii Sports, and was a profitable hardware sale from day 1, where the other two banked on loss-leading for market share and making it up with a high attach rate. Definitely a fad, but also one that printed money.
All three did well enough to keep going, but they're really apples and oranges stories.