Having the best of both worlds means being lucky enough to enjoy the benefits of two situations that are supposed to be mutually exclusive. For example, if a research fellow at a university has the best of both worlds, she or he is able to enjoy the lifestyle and salary of a professor while keeping the freedom and flexibility that students normally give up when they get jobs.
Both "what is better" and "which one is better" are correct, but the choice between these two phrases depends on how specific you want to be in your comparisons. For instance, "what is better" is appropriate when comparing categories or concepts and broad ideas, while "which one is better" is usually employed when examining individual items or choices within a category.
In the case of "which is better," the word "better" denotes a quality that is optimal when compared to something else in a particular context, such as within a time frame or versus a competing product. For this reason, it's important to be clear when posing questions and expressing preferences, especially in writing. Choosing the right phrase can make all the difference in your communication. For more information about writing clearly, read our article How to Write Well. Using the right words can also help you express your ideas more effectively and avoid confusing others. The best way to ensure your clarity is by reading extensively and learning as much as you can about the language in which you write.