Once you get above the 57- 58 Rc hardness, conventional files skate across the surface of most steels. Some alloying elements will help create this skating effect. At 60 Rc, you are getting into needing silicon carbide stones to efficiently cut into most hardenable steels at hand speeds. Many steels will not get this hard regardless what you do. Carbon content is a major key.
Toughness is the ability to take impact and that suffers the harder you get. The other test they do often on the forged in fire series is a bending test. This also suffers with increased hardness and why most knives are kept in the lower 57- 58 Rc range.
Saw chain is a compromise. On most quality saw chains, a lower carbon steel (soft enough to file) is used so it will stretch -bend rather than break, and the cutter links at slightly harder and are chrome plated to give them a harder edge. Chrome is much harder (up to 70 Rc) but its thinness (typical hard chrome .001-.003") still allows files to work. Edge quality suffers a bit and as many have experienced, always leaves a bit of a feather (burr) after sharpening that dulls or rounds off the edge quickly. Older wheel grinders would allow you to reverse grinding wheel direction to help reduce this burr. A dremel tool is great tool for real hard chain that your not cutting into with the hand file.
Once the edge is rounded slightly, it needs a touch up. If the corner -edge will not catch your finger nail with slight contact, it is dull. If you want the most durable chain, the ones used in demo or by fire departments are a option as Hill mentioned before. They braze a thin carbide shim to the top of the cutters. You need diamond files or diamond wheels to sharpen them and you need to keep steeper (more square) grind angles as the edges get brittle if tapered too thin. Their efficiency suffers a tiny bit because of this, but they will cut through wood with nails in it for a bit and not seem phased by it.
As far as hand vs machine sharpening goes. Always, the best edges -with max hardness maintained, will be gotten with hand speeds. Wheel grinding to get close, and finish by hand if you want the best - fastest cutting edges.