The original on the KLR650 is 12v, 14Ah alright.. the only prob with using a 12v 12Ah battery is that it may not be able to start the bike as well as you'd like on those cold mornings because of the smaller "cranking" capacity. A 6Ah battery is a tiny capacity.. I'd imagine thats only suitable for 250cc bikes or smaller.. not sure though.
Once the bike is running, there should be no prob at all, unless you overload the alternator with accessories, in which case, the battery will die more quickly than with the 14Ah in, and the bike will die sooner as a result.
You're not running any third party CDIs or anything else that takes the power from the battery, rather than the (second) pickup coil? Stuff like this increases the dependence on the battery, so a good battery is even more important.