Here's a software engineer's (and amateur game developer) perspective:
Usually your best feedback comes from outsiders, because they come with a different perspective. That being said, you will get useful information from just about every type of beta tester. Diversity is the key. The biggest mistake anyone can make with anything other than a marketing beta (which really isn't a beta at all) is to limit the participants to only a select few types of players. Notice that a release that is primarily for testing (bug squashing) is also different than a beta. Those require a very select group.
Usually your best feedback comes from outsiders, because they come with a different perspective. That being said, you will get useful information from just about every type of beta tester. Diversity is the key. The biggest mistake anyone can make with anything other than a marketing beta (which really isn't a beta at all) is to limit the participants to only a select few types of players. Notice that a release that is primarily for testing (bug squashing) is also different than a beta. Those require a very select group.