It’s a very interesting question. I think there’s great value in both situations, although the value changes generation by generation.
Growing up, I only invested in the Nintendo ecosystem. As a result I dug very deeply into each console’s library and spent hours and hours exploring every corner of each game. Later on, I invested in Sega, Sony, and Microsoft platforms, and as a result obtained a much fuller, more comprehensive understanding of what was out there. The cost: I had to move on quickly after finishing each game, and bypass certain games altogether. My experience was wide but shallow, where it was previously narrow but deep.
Which one is better? I’d argue the multi-console approach, especially if you are, like me, someone who wants to explore as much of the medium as possible.
Lately, though, as a result of getting older and having less free time (and because, for me, Xbox and PlayStation are increasingly superfluous) I’m seriously considering pulling back and focusing just on Nintendo again. Will I miss a handful of GOTY contenders? Surely. But, for the first time in about 20 years, I think I can live with that.