Your examples seem slightly wack:
"For example in engineering you would have chem eng at one end and maybe mechanical or something at the other"
OK, I don't know from engineering, but mech is pretty high up there. The low prestige engineers are probably civil engineers, not mechs.
"Doctors would have a scale that goes from, say, brain surgeons to (just guessing) podiatrists."
Fun fact: the low end of prestige is probably GP's. Podiatrists are specialists, and there's prestige in that. Some of them even perform surgery, which is worth considerable prestige. Very high prestige goes to medical researchers. ("Research" is a high prestige modifier to many fields. Consider engineers vs. research engineers.)
"In the military it would go from (probably) fighter pilots or Delta Force to basic infantry."
These actually depend on the individual military service, aside from certain generalities (combat people are higher prestige than support people, command is higher prestige than staff). As a result, infantry would actually be higher prestige than, for instance, mechanics or supply.
Army, I couldn't speak for. I know Rangers and Special Forces and Airborne are higher prestige than "leg infantry", and the cavalry were high prestige in their era, but I can't say for sure.
Navy is hard to say, since there's a rivalry between aviators, surface guys, and submarine guys. But all three of those can be unrestricted line officers, and that's the higher prestige track since it leads to command. If I had to hazard a guess I'd say the aviators have the edge--they command the biggest ships, and ever since WWII it's been demonstrated fact that the real power of the Navy lies in its air.
Air Force is run by the pilots, obviously. Combat pilots over cargo pilots.
Believe it or not the highest prestige component of the Marine Corps is probably the infantry. Everything else is there to support the infantry. Added to this is that every Marine is trained as a light infantryman, and every Marine officer is trained to command a rifle platoon. The Marine Corps doesn't really operate on these terms much, as they simply consider the entire Corps to be the best part of the military.