I have tried many gallery plugins: NextGen, Envira, FooGallery, Meow Gallery. . . This is by far the best! Why do I say that?
(1) Support. I get better support from the developer (who I believe is in a one-man shop) than I have from the "big guys."
(2) Customability. You cannot possibly have a more customizable gallery plugin than JIG.
(3) Uses the native WordPress galleries. JIG enhances the native WordPress galleries. It is my understanding this causes fewer conflicts with other themes and plugins.
Now, for a totally fair and balanced review, let me state what I don't like about JIG. (To be fair, this isn't enough dislike to take away even part of a star).
(1) It's not the most user-friendly gallery plugin. This is a side-effect of JIG being extremely customization. Interfaces tend to get more complicated when there are more options.
(2) The documentation is not the best. I understand the developer is working on the documentation, but at times, it can be unclear exactly what to do, even if you're reading from the "manual." Just ask a question in the comment, and the developer will help you out.
Overall, I think this is the best gallery plugin for the WordPress ecosystem.