Synthetics have the same physical and chemical properties as natural, but will typically have telltale inclusions seen under magnifaction. They will price less than natural sapphires of equal color quality and there are different levels of quality you can get with synthetics depending on which process is used. (Chatam being the one of the finest, and flame fusion being at the lower end).
I personally have a natural sapphire in my engagement ring, and I must say the color is quite unlike any synthetic I have ever seen.
I would suggest looking at a few in person and deciding for yourself what appeals to you. My favorite website for gem stalking is palagems.com. I find their pictures are very true to irl, as is not always the case with many colored gemstone websites.