If used metaphorically or figuratively, they are basically interchangeable. For example, "Her attitude was a huge obstacle for me" and "Her attitude was a huge hurdle for me" mean the same thing. If used literally, a hurdle is usually something that you have to jump over, mid-stride, while an obstacle might be something you have to swerve to avoid.

If you are not specifically talking about the 110 or 200 meter hurdles in track, 'hurdle' means exactly the same thing as 'obstacle'.