Fedora uses SELinux whilst Ubuntu uses AppArmor out of box. Both are secure enough but SELinux is a lot more powerful.

SELinux is so wide it permeates everything, it potentially labels every object in the system and conceptually elevates the system to a more sophisticated security infrastructure, it allows you to implement all main security paradigms in access control theory; even military and government organizations can use it for their strict security needs. With SELinux it is possible to implement MAC (“Mandatory Access Control”), MLS (“Multi-Level Security”, with Bell-La Padula and Biba models), MCS (“Multi-Category Security”), RBAC (“Role Based Access Control”), TE (“Type Enforcement”). Besides, SELinux is based on the default deny principle.

AppArmor, on the other hand, simply lets you define what a single application can and cannot do, according to the principle of least privilege but without the implementation of complete security paradigms.

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Regarding package testing both have QA tools and large user base, but I speak from my experience when I say that Fedora packages are more secure. I had a lot more breakages updating Ubuntu. Maybe it's because Fedora is much more up to date... who knows.

However, Ubuntu has better hardware support and a larger user base which in turn means better support if you encounter a problem.