How to know which archive page is active

First of all, is_archive() does not accept any parameters if you have read the codex, that is why it will always return true no matter what you tried on any archive page

As pointed out is_post_type_archive( $post_types ) is the proper conditional tag to use to check for a specific post type archive page.

One thing though, your question is unclear on how you would like to use this condition, as you already have an archive page specially made for each custom post type, so to check if your on a specific archive page would not make sense. is_post_type_archive('blog') will always return true on archive-blog.php while is_post_type_archive('product') will always return false, and is_post_type_archive('product') will always return true on archive-product.php while is_post_type_archive('blog') will always return false.