The resolution of the two versions is the same but the size is different as the JPEG compression is different. Depending on the subject, it should require a closer inspection to actually see differences with the naked eye.
Another difference is that in the “web optimized” version the meta data has been removed:
Note that the original version even has the GPS coordinates included, so you can find out where the image has been taken. I guess that many users posting to theta360.com are not aware of this potential privacy issue.