I do recall now that "save to web" in Photoshop™ deletes exif.  Should have known. 

I tried in PSP and the JPG Optomizer works similar to "save to web" and eliminates the exif. Saving straight to jpg keeps the data in the image.  You click options in the save window and set the compression level..not as easy as in Photoshop but it works and keeps the exif embedded.