The Experience Point economy is, for me, one of the foundational aspects of Old School play. I'm far more likely to tinker with how XP is generated, consumed and flows than I am, say, the combat or magic systems. I'd even profess that most of the traditional parts of Old School design can be dropped, but as long as the XP system remains it still "counts" as old-school gaming. Well, that and reaction rolls, random encounters and morale ... basically, the real meat of play are those core systems generating interesting situations; combat is just a detail of negotiating the results.
But that's all to be hashed over more thoroughly another time. For now, I've been comparing formula for Swords & Wizardry, my preferred retro-clone (specifically White Box). Look, I even made charts!
A common alternate method, derived from the original 1974 D&D rules, is to just give a flat 100 XP per HD of defeated foe. It requires no chart look-up, and many GM's like it because it gives low-level characters a comparatively big boost while throttling back the advancement of higher level characters. I dislike it because I think it makes minor monsters so valuable (a mere score of orcs is worth more than most dragons on the RaW scale) that it'll encourage characters to stick to hunting unchallenging rabble and minions after they should be powerful enough to take on bigger targets.
The third method on the chart, "HD² x 10," is a formula I came up with when running Stars Without Number, a game which has a very broad approach to XP rewards and no specific scale for foes defeated, something I found a bit too loose. I've since come to like it enough to port it over into other OSR games because it produces awards passingly close to the original scales (well ... it evens out in the long run) and since it's a consistent formula I don't need a chart to calculate awards. The only quibble (a minor one, but it might annoy some) is the numbers generated can scan as somewhat inelegant, such 810 XP for a 9 HD monster, or 1,690 for a 13 HD beast.