nadhifa,
paleontology is a general term for the study of some aspect of an ancient environment. Some scientists look at ancient pollen grains (paleonology) to determine what kind of trees grew during a certain time, which also gives clues as to the climate. since you are interested in birds, you would be studying bird fossils, maybe attempting to excavate them from certain sites, based on other scientists finds.
with ornithology, you could research many aspects of birds - 1) at an individual level, such as physiology flight adaptations, diet preference 2) at population level -migration patterns, territorial behavior 3) community level such as interactions and their effect on other species besides birds in their environment 4) evolutionary aspect, such as looking at bird bone structure in existing birds and then looking at fossilized extinct birds
I guess it depends on what you want to spend the most time doing. I think there are probably more opportunities in ornithology, because you wouldnt have to be so specialized and if you were at a university you could teach field courses etc.
by the way, when you are talking about the person who is in a certain job, you use the ending "ist" so, someone who studies paleontology is a "paleontologist", ornithology is "ornithologist"
