It is just the difference between British and American spelling. Use whichever you please, but be consistent.

The termination -tre belongs to the American spelling, while the other is British. The same happens with, for instance, "colour" and "color", as well as many other examples. Whatever you chose, use it in the same spellig in the context you are using.

In the United States, "theater" is the most common spelling, but "theatre" is an alternate spelling. It is so common that the dictionary just says "or," not "usually British." Quite a lot of theaters use "theatre" in their official names. The Shubert Theatre, the Theatre Guild; etc. To U.S. eyes, that spelling looks European conveys a sense of style and elegance. The dictionary (AHD3) also lists "centre," while identifying it as "usually British." Once again, it is used because it looks elegant. Houston has a "Citycentre" (one word). In the little town of Lynnfield, Massachusetts, USA there is a "Centre Yoga," probably named because it is on a street named "Centre Court."

To answer your question directly: if you are just learning English, I suggest learning and use the British spellings. In the U.S. they don't look uneducated, they just look, well, British. If you actually plan to be using U.S. English, then use the U.S. spellings. In real life, a computer spelling checker will take care of this. You can't rely on it for things like "whether" vs. "weather" but it can be used to correct British spellings in the U.S. or vice versa.