Modernly, alot of times when the 13th chord is played and the 11th is there too. It is sharp. Looks like this Cmaj13(#11). To me it doesn't sound quite as dull, or vanilla sounding as the regular 13th. In this case I usually ommit the 7th (esp in the maj and m versions), and then use the D7 chord that exists within the chord as a pedal, while playing the regular C major chord somewhere over the D7 pedal. Or vice versa.

Another version where this chord comes into good use, is having one hand play a steady rhythm of one of the chord in broken form. While the other hand stomps out the other chord. On guitar you could have one guy just pick a C major chord, and you hit a D7 chord.

It's great for the use of modulation as well. Here's an example.


1h| Cmaj . . . | % . . . | % . . . | % . . . | Gmaj . . . |
2h| Cmaj . . . | Em . . . | Am . . . | D7 . . . | Gmaj . . | and so on...


Here the 1h underlines the key center, while the 2h plays a harmoney based around that key center. You could continue this with G maj also to create a modulation sequence.
Or if you don't want to ommit the seventh, you can play a Bm7 chord instead of D7.