Why do some lamps have different power ratings for different kinds of bulbs?
Different bulbs dissipate heat differently

The reason why you see different power ratings for incandescent vs. self-ballasted (LED, CFL) lamps for a given fixture is because the different kinds of lamps dissipate heat differently.  Incandescent bulbs give out large quantities of heat, but most of it is dissipated from the bulb as infrared radiation -- this escapes the fixture as long as it is not blocked/absorbed by parts of the fixture.

However, while self-ballasted lamps generate far less total heat than incandescents, most of that heat is generated in the lamp base area and must be conducted out.  This leads to "heat trapping" in some fixtures that are not able to conduct heat away from the lamp socket area well, and limits the ability of the fixture to handle higher power LED/CFL bulbs.

The answer is to find fixtures that aren't so stringently limited -- I, personally, would be inclined to integral LED fixtures in this day and age vs. Edison-base designs to begin with, as using Edison bases for LEDs inflicts many compromises on the both fixture and bulb designers, vs. the design freedom and performance capacity possible with fixtures designed around LED technology.