First, be aware that your present card is a single slot item, as most were
back then, but the 560 is dual slot. It only uses one set of sockets, but
occupies two positions worth of card space. This can come as a surprise,
and you must ensure you've got room to fit it on your MB. (An important
consideration that is sometimes forgotten among all the other technical
details).
I can't claim any great expertise in card performance, other than what I
glean from a pretty cursory examination of the summaries at sites like the one
I linked in the previous post, nor am I fluent in anything to do with dual
monitors, such as whether there is any benefit from using them with CoD, so
I can't say what sort of benefit you'll gain from the 560 over the 550
other than noting it sits three bands above the latter in the hierarchy map
I linked, which means you would notice the difference. The second digit in
nVidia product numbering always indicates performance, higher being better,
8s and 9's being top gamers, 5s and 6s adequate gamers, 2s (I can't remember
seeing 3s) being generally not enough muscle.