There IS a noise cancellation effect produced by pair twisting. However, the primary goal of this twisting is to eliminate crosstalk and capacitance between the pairs of the cable, NOT noise from external sources. I have heard claims that twisted pair eliminates RF tranmissions as well. However, if you've ever installed high-grade unshielded twisted pair anywhere near a radio station, you know that this is complete bull. That goes for 110/220 volt power cables as well. In a high noise environment, sheilded twisted pair (grounded on one end only) or fiber optic is the ticket.
In less harse environments where ordinary unshielded cable can be used, the performance difference between a CAT6 install and a CAT5e install may only be seen with a Fluke testor. In fact, I would be inclined to say that the difference between an OK install of CAT5e and a superior by-the-book install of CAT5e would reveal a more dramatic difference than the performance delta of CAT5e to CAT6.
Also note that THERE IS NO SPEED INCREASE with CAT6. Network speed is based on the network interface cards, switch/router interfaces and of course the cabling. If everything in your network is 100M (or even Gigabit) and you are using properly installed CAT5e, "upgrading" to CAT6 won't make a bit of difference.
There are very slight downsides to CAT6 as well. For example, the cable jacket is a lot heavier and tends to fill up conduit a lot faster. It's a slight pain to punch and a huge pain to skin. The cable doesn't bend as easily either, partially because the copper is a slightly heavier gauge. Why? Because as you increase the number of twists per inch, you also increase the length of the wire (think of a helix in space). Longer wire = more end to end resistance. This is combated by increasing the diameter of the copper, since electrons flow over the surface of the wire...not through "the middle". Greater surface area is the whole reason why stranded wire is used in some applications.
Now with copper prices being at an all-time high, upgrading any existing cable should be looked at with a critical eye. For a CAT6 "upgrade", you will not only have to replace the cabling, but the patch panels, patch cords and every single jack as well. Add in installation labor, and I think that cable replacement in an existing CAT5e environment is no longer a compelling argument.