Do they have any advantages over the regulars?
Not that I know of, well, maybe they can withstand heating with your soldering iron a little more than a "normal" diode. That is a form factor that was popular or widely used back when SILICON diodes OTHER THAN teeny 1N34 Germanium diodes first became available. The manufacturers probably perceived that folks who were not used to diodes being able to handle anything in terms of current (eg; used for radio detector use only) wanted to see heat sink, they wanted to see heavy-duty. Remember that there was not especially the need to make everything super small like it is today. When those diodes first came out, most other devices in a piece of equipment were probably tubes. For various reasons, that form factor has persisted. One reason is that those diodes could be mounted in metal clips much like the ones used for mounting fuses to a PC-board. MIL-spec applications usually mounted them that way, for the anti-vibration mechanical strength.
Incidentally, just because that diode is big and metal-cased does not mean that it is high voltage. It has a number printed on it, Google that number and see (and stay within) its specs.
Now we have 1N4007 1000 volt 1 amp diodes in a package the szie of a 1/4 watt resistor. In my opinion, if you went back to 1958 with a 1N4007 nobody would believe you that that little thing could handle 1Kv.