Advantage in size on most logs to putting the heart up, of course. Additional advantage in that knots originate at the heart, so if you don't want them, you can run the cut through the middle of the old branch as you run it through the center of the log. You also want to watch the direction of growth on the tree, so that you can avoid the branches which angled upward by chosing your crosscuts carefully. Other factors, if knots aren't, are the moisture load in one lying for a while, and heart checks, which are common in woods like cherry and soft maple.
With the heart up, you'll want to leave the first few years behind. That's because the curvature of the annual rings causes greater proportional distortion when drying, sometimes resulting in splits from the heart into the walls of the piece. With the heart up, you can expect the sides to drop pretty much to the averages listed for the species under radial shrinkage. The tangential is going to be much less than the average listed unless you leave a very broad bottom, because there's less continuous wood. Makes another good reason to taper to the bottom, as is also faster drying with water lost ten times faster out the open end grain than diffusing through face grain.
If you have large trees, as urban folks can find, you may elect to put the heart down at the bottom, but you get a couple of bad things for the good of not having dark blotches on the rim. First, you get greater stress from the smaller radii of the annual rings near the bottom, which can sometimes pull the whole thing out of whack so far you can't get back to round with a thinner rough. Second thing you get is pick-out as you cut down inside the bowl. It's fairly easily controlled, but can be annoying if it happens in the wrong place at the wrong time.
