What does "compared favorably to" mean?

Compare, like many other verbs in English, can be used transitively and intransitively. As with a lot of English verbs, its intransitive usage is much similar to its main transitive usage in meaning. For instance, we can say "A person grows those plants well" as well as "Those plants grow well." As a learner you are understandably more familiar with the transitive sense, but you should also familiarize yourself with the intransitive usages of these words so that you won't be thrown off when you encounter them.

Merriam Webster gives:

intransitive verb

1: to bear being compared
The two don't even begin to compare.
We bought two different brands of peanut butter to see how they compare.

If A compares favorably to B, A is considered at least as good as B. So this sentence means

These are the latest signs of growing worries in Europe after the continent (Europe) initially (at first) fared well (did an OK job) compared to the way the US handled the virus.