When I upgraded from PS3 to PS4 I had to keep my PS3 to further have access to my PS3 games. Only a few cross-buy games I bought for PS3 (or got via PS+) I can play on the PS4 and some cross-generation games I would have to buy again to play on the new system.
When I upgraded my graphic card last month to a GTX 970 for 290 € (shipping + taxes included), I didn't have to keep my old card to play older games, I was able to sell it for ~100 €, so the upgrade costed me less than 200 €. Although Dead Rising 3 PC is a crappy port, I was able to play it in 1920x1080 (twice the XBO-resolution) with 50 - 70 fps (twice the XBO-framerate), so you don't need a 1000 € GPU for that. And not only new games profit from the performance upgrade, but also every 6th and 7th generation multiplatform game... you don't have to buy them again to play them in higher resolution, with better antialiasing (or with downsampling), with additional effects (PhysX on max, etc.) or evenbetter textures (mods).
If you start from scratch, a console is cheaper (at least if you don't buy dozens of games each year), but if you already have a decent PC, a simple upgrade is cheaper in most cases.
