The strength in bending of any beam is related to the moment of inertia of the beam, which for a rectangular beam is equal to 1/12bd^3, where b is the width and d is the depth, and ^3 means cubed. For a triple 2x6, where each 2x6 is true measure 1.5 inches wide x 5.5 inches deep, the moment of inertia is 62.4 in^4.
For two 2x8's, where each 2x8 is 1.5 inches wide and 7.25 inches high, the moment of inertia is 95.3 in^4. The doubled 2x8's therefore have about 50% greater moment of inertia than the tripled 2x6. The actual beam capacity is a bit more complicated to compute, since we are primarily interested in extreme fiber stress due to bending.
In bending, the doubled 2x8 could support 264 lbs/ft on a 10 foot long beam assuming an allowable stress of 1500 psi. For the same allowable stress on a 10 foot beam, the tripled 2x6 could support 228 lbs/ft. So the doubled 2x8 beam can support approximately 15 percent greater load per foot than the tripled 2x6 beam, assuming the same maximum allowable fiber stress.