The PS3 saved its terrible start by releasing really good exclusives. I did most of my gaming on 360 last gen but still got a PS3 because of the top notch exclusives. Lack of interesting exclusives is why I will most likely never buy an X1. The play anywhere program is sweet but even if that didn't exist I wouldn't buy their hardware for what's available currently.
I didn't get around to playing Gamecube games until the Wii. Great exclusives on both of those consoles as well.