Arthur is correct. You are shooting wide open @ f5.6 on the 55-300 f4.5-5.6 and the 55-300 needs to be stopped down a
stop (as do most
lenses) to f8 to get the best
sharpness and then possibly more if you want some
Depth of Field as at even f8, there is little
DOF at 300mm and f8. The trouble with stopping down even further is that you end up requiring a higher
ISO meaning that will take the edge off
sharpness as well. Welcome to the world of balancing
shutter speed/
aperture/
ISO.
With the 300mm photo, you have shot at 1/1250sec f5.6 and
ISO 100, where you may get away with 1/600sec, f11,
ISO 100. You do have VR on that
lens, so you can safely shoot at an even slower
shutter speed, maybe even down to 1/50sec with good technique, the only drawback is that any subject movement will then appear, like the waves will possibly be a blur. Again, you need to balance your
shutter speed to whether subject movement is an issue. However, a little blur on wave movement may be a good thing to show motion.
The other problem with this comparison, is that isn't the
Sigma a macro
lens? If it is, then it is a VERY
sharp lens and possibly not a fair comparison with the 55-300 f4.5-5.6 kit
lens!