Games on a console vs on a PC is always a hot topic for discussion/argument.
Games that are released for/on a console are, in general, more stable. There is only 1 set of hardware they have to make it compatible with. Add another console or two and they need to check 3 sets, but still very simple to do and easier to make a stable game when a lot of the variables can be controlled.
PC gaming on the other hand introduces a TON of variables. The hardware variable alone is staggering when you think about the various CPUs, graphics cards, RAM, Motherboards, Hard drives/SSDs, keyboards, mice, etc ... that can all cause a game to not work for a particular user/group of users. It therefore becomes much harder to build a stable game for PC versus for a console.
That said, it does not mean that many studios don't put out awesome PC games, because they do, and in bountiful amount, far more than you will find on any console. Plus on the PC you can get so much more quality and performance out of the game (depending on your computer) than you could from a console.
Will a new graphics card increase your capability to play new games vs what you have now? Possibly, we don't actually know what you are running to know how big a jump you're talking about. If Black Ops 3 is what you're mainly wanting to play and it's not optimized very well for the PC, then no, maybe buying a new graphics card isn't the right move and you should pick up a console (or the game for the console you have). If you're wanting to play more than just BO3, if you're wanting to get better FPS and quality than you can from a console, then yeah, maybe a new graphics card is just the right ticket for you.
For what it's worth, if you get a new graphics card, you will probably need a new PSU too.