I'm cheap. A tile tool costs me about $5 or so to make for a typical 8-10" mirror while the glass for a tool will cost a lot more than that - usually about half the cost or a bit more than the pyrex mirror blank. If you are already doing a plate glass mirror, the cost is another blank of the glass.
For one off and never again, a glass tool may be a bit cheaper as the cost for the tile tool components are going to be spread over several mirrors.
As to the ring tool for making the hole, the purpose of that is to dig out most of the glass and if you don't do a really even job, a few wets of work with the tile tool takes out any of the errors left with the ring tool. The tiles aren't very thick and thus, the need exists to remove as much material as possbile in order to minimize the need for glass removal to keep the wear on the tile to a minimum. I usually consider that a mirror is ready for a tile tool when there isn't much more than a few paper thicknesses at any point of the curve that was generated if you do a curved template for measuring your ROC or a few thousandths of an inch when measuring with a spherometer over the surface. That much error of the spherical condition will quickly be taken care of by the tile tool without any error.