In order for artwork, especially vector artwork, to be "pixel perfect" the anchors and paths need to rest on the pixel grid properly.
It is exceptionally customary for all applications to not alter artwork upon export - beyond anti-aliasing or color profiles. In fact, if an application's export feature were to alter the core construction of artwork ...
I'm guessing that the anchor points of your friend's logo follows the pixel grid:
And that the anchor points of your logo doesn't and has decimal coordinates:
If the contours of your vector shapes lies between the pixel grid, anti-aliasing will be introduced.
I went and checked the author's video tutorial mentioned on another answer, the process is actually quite simple if all you want is a simple 3D shape for a logo with no textures or shadows:
create the donut shape (draw a circle, 3D > Revolve... and adjust the offset)
create a symbol with both texts offset as shown below
edit the 3D effect, check Invisible ...