Pull Requests builds are useful in answering the question “What if this PR merged into target (base) branch”. Feature branch (other terms are source or head branch) build is not enough to answer this question, because while PR was developed some other commits could be made to the target (or base) branch.
During PR build AppVeyor merges PR with target (source or head) branch safely in transient build environment and runs required build scenario. Scenario itself can be altered in many ways for Pull Requests builds with project settings (like Pull Requests do not increment build number) and specific PR-related environment variables (like APPVEYOR_PULL_Requests_HEAD_REPO_BRANCH).
AppVeyor supports GitHub Pull Requests builds for years. Now we added Bitbucket Pull Requests support. For new projects it should work out-of-the box. For existing ones AppVeyor project webhook should be updated so the following Pull Requests events added: Created, Updated, Merged, Declined. To set this, navigate to your Bitbucket repository Settings tab, select Webhooks, find AppVeyor project webhook and press Edit.
If you do not need Bitbucket PR builds for new projects, uncheck those Webhook setting, so AppVeyor will not be notified of Bitbucket PR creations and changes.
Best regards,
AppVeyor team