Different image sizes for home and post pages

If your talking about the images that are written into $post->post_content (the_content()) you’ll either need to write a filter that strips out all images and replaces them with the smaller version. Or you could just use CSS. For CSS make sure you have body_class() in your body tag then you can localise a maxwidth to your home page.

body.home .post img{
    max-width:300px;
}