tinypic is actually PhotoBucket and their privacy policy stinks.
Quote: "Contacting You for Offers and Promotions: You agree, in consideration for the use of the Services provided by TinyPic, to allow TinyPic to use your personal information to send you marketing and promotional materials. TinyPic may also send you marketing and promotional materials that promote third party products. "
While PostMyImage promises not to use or pass on your info, you should keep an eye on the policy, because it will probably change as their bandwidth bill gets bigger.
Best.
I'm sorry, my answers are limited. You must ask the right question.