Two of the three (power vent and chimney) rely on internal air for combustion, a direct vented system utilizes outside air for combustion. A direct vented system just by that one fact, will be more efficient since you aren't throwing away internal, already heated air, outside and having to heat the new air coming in to replace it.
A power vented system has numerous additional safety devices in it that all must be working to allow it to run. A natural vent up a chimney wouldn't know if the chimney ended up being plugged, and was dumping all of the combustion products into the house (you might not either after it killed you!?). Even on a chimney, you might add a damper to help efficiency, and that, being mechanical and in a hostile environment, can fail.
Not to say that a direct vented (closed combustion) system doesn't have safety features, but of the choices, they can be the most efficient.
Not sure if they make a mod/con oil burner, but if you have NG available, that likely would be your best choice, should you decide to make the switch. You can do some searching here and see some of the recommendations - the first thing would be to get (probably pay for) a good manual-j (heat load) analysis. The existing boiler is almost certainly oversized, probably by at least 2x and maybe lots more. Any new system should be properly sized for maximum efficiency and comfort. Ideally, on the coldest day, the boiler should run continuously. And, with a mod-con, it has the ability to run continuously on more days than a fixed output device. This allows it to attain its best comfort and efficiency.