Will a pokemon that I have evolved have higher CP/CP CAP than one of the same pokemon that I have found in the wild? Will a pokemon from an egg have higher CP/CP CAP than one in the wild?
/u/transphenomenal plotted the data, in this comment. The following is a roughly normally-distributed graph for naturally caught Pokemon, where 100 indicates a perfect IV Pokemon, with the highest possible CP cap, and 0 indicates a perfectly bad IV Pokemon, with the lowest possible CP cap.
This graph shows Pokemon hatched from eggs:
There isn't a difference. Every Pokemon of the same type (e.g. every Pikachu, Charmander, Squirtle etc.) Have very similar growth stats. The CP cap on every Pokemon is based on the Trainer his level. Catching a Pokemon with a higher CP simply makes training cheaper.
So far the only difference in growth stats is if the Pokemon is XS or XL which can be see in the Pokemon's detail page. XS increases max HP but decreases max CP, XL does the reverse.
No, however you are rewarded substantially more for hatching an egg than catching that same Pokemon in the wild - you receive a random amount of stardust that seems to range from about 500-1000 and a random amount of candies (I've gotten from 6 to 21). You also receive more experience.
EDIT: Research by people from TheSilphRoad suggest that Pokemon from eggs actually have higher IV's on average