Both will provide a nice roof with completely different appearances. The 3/4" Natural Split will also be called a handsplit and the thickness would generally be 1/2"-3/4" in butt thickness and will provide a random shake appearance of different thicknesses. While a tapersawn would be very uniform in thickness with all the butts being identical and tapered down very thin.

And a picture of a "handsplit" shake roof.

Then there's the third choice: faux. ;^)

As a follow-up:

Has anyone worked with "Perfection" shingles? I gather it does give a tighter look. My contractor feels that they are very thin and they might not hold up as long.

Has anyone put on Perfection shingles? The look seems interesting to me.

I have perfection and my roof is 25 years old...looking now to replace with tapersawn.