Which lens is sharper with TC-20E III: 70-200mm f/2.8 VRII or 70-200mm f/4 on D800/E

thanks Kanano.  I read the site and it was very helpful.  I have pretty much decided that the 300mm F4 with the 1.4X is better than the 70-200 with the 2X.  Now I'm just wondering about renting the 300 mm f2.8 lens for a week in Costa Rica.  Either that or the 300mm f4.  I know that the 2.8 version is much better but I'm not sure I can handle its weight.

Marsha