Which Theory is right: Einstein's Gravitation theory or Isaac Newton's gravitation theory?

For the most part, Newton's theory and Einstein's theory make predictions that are almost identical. But there are a few cases where they differ slightly in their predictions, and in those cases you can do experiments to see which one provides the more accurate description. * Newton's theory predicts that gravity will have no effect on a beam of light. Einstein predicts that gravity will make light beams bend slightly. In 1919 an experiment was done that showed that a beam of light passing by the sun, got bent by exactly the amount Einstein predicted. * Einstein's theory predicts that something that moves fast and close to a very massive body (like Mercury around the sun), should find its orbit perturbed in a way not predicted by Newton. Measurements of the orbit of Mercury show that its orbit is perturbed by exactly the amount Einstein predicted. * Einstein's theory predicts that gravity should cause time to slow down; Newton's theory does not. Careful measurements of clocks in gravitational fields show that they slow down by exactly the amount Einstein predicted. So, there's very good experimental evidence that Einstein's theory is more accurate than Newton's. However, this does not at all mean that we should abandon Newton's theory. A good reason to keep it around is that, for most purposes, it gives results identical to Einstein, while using math that is much, much simpler. So you can think of Newton's theory of gravity as being "an extremely useful approximation."

Both and neither. One day scientists will come up with a theory which supersedes Einsteins. But at present Einsteins is more accurate but for 99% of everyday use Newtons works out just fine.

Newton's gravitation is a special case of Einstein's theory.

Both are used because both are right. Newton's theory works in every day situations, eg. macroscopic bodies. Whereas Einstein's improvement of the theory allows it to be used with microscopic bodies or bodies travelling very fast (ie close to the speed of light-usually these are only microscopic anyway!).

In most situations Newton's descriptions work extremely well. But under certain extreme conditions, relativistic effects will become noticeable. They are both correct.

Einstein's theory is currently accepted as being 'correct'. However, as you said in the question it is also more complicated. Newton's theory, despite being wrong, is highly accurate for almost everything. It is only when observing something very close to a strong gravitational field (such as a black hole or a massive star) that even the slightest difference between the two theories occurs. This is due to effects laid out in Einstein's theory, such as the slowing down in time in strong gravitational fields. Remember that Newton's was accurate enough to be considered fact for 100's of years, so obviously it is VERY accurate in almost every situation and is still used often because it is so much easier to get an answer.

Newton's theory is all based on observations of planetary motion etc and is still effective on the macro scale for most calculations. Einstein's theory looks at small sale micro objects and supplements ( but not supercedes) Newton's formulae.

Although both of the theiories make sence i prefere Newtons due to the simplicity and the obvious. it explains why a apple wouldnt fall up towards the stars, as einsteins is a bit more complex and more vauge.(sorry about spelling)

Under most situations Newton's law of gravity is accepted . Actually I am on an anti-gravity machine right now, A chair, ha.