Migrating Posts to Different WordPress Site

I would like to migrate all of my posts from one site to another.
Using the wordpress import/export is not working properly with images.
After I import the exported posts the images are in the posts but they are simply linked to the old site. The images were not downloaded to the new site even though I told it to download. Also no featured images were transferred over.
So what now?
I would like to simply copy the uploads directory over to the new site and have the posts associate their URL’s properly.
How do I go about doing this?
Is there a better plugin that will import/export my posts properly available?