Both have uses and both have drawbacks. Tinypic's drawback is that it seems to want to bombard users with pop-ups for the privilege of using their hosting. But using it is very simple when in a pinch. http://tinypic.com/
Photobucket.com has always been user-friendly and easy to work with, but unlike tinypic.com, Photobucket has a carrot up it's rear pertaining to large images. Not large filesizes, mind you -- Just large pixel widths. Photobucket automatically compresses large pictures to a size of no larger than 640x480, even if the filesize itself is not that large. But the service is free, so who can really complain.
I've never heard of tiny pic before, but I've used photobucket for at least 9 years and I've always liked it, if you're putting up a pic for a board it's a great site to use since it does resize automatically.
____________________ The dead do not squeeze and please....