I have Belden Cat5e that says "Tested to 350MHz" right on the cable.  
 
How does that compare to Cat6?

I would really look at the labeling because Cat 5/5e provides for performance of up to 100 mhz and cat 6 provides for performance of 250 mhz.  

Uh.. Cat 5e can be certified up to 350mhz. Cat 5 is official, Cat 5e was created for places like universities and such.
 
You can certifiy your own cables - You need the equipment to find the range. All they're saying is at the time of testing it was able to sustain 350mhz.
 
The only reason to switch from Cat 5e to Cat 6 is mainly distance and high quality gigabit.

Prove to me that Cat5e will support 350 mhz.  Find me the specification and which section of the specification say it will support 350 mhz.  Not because some manufacturer say their Cat5e cable will do 350 mhz.  
 
Twisted pair is twisted pair.  No matter if it's cat 5e or cat 6, I don't believe there is any distance gain from one to the other.  The difference comes in the bandwidth support.  

350mhz??  Is it even possible??  
Going to have to google this.