When you pick a video, you get the option to watch it (obviously), but you also have buttons for related videos, to add to favorites or a playlist, and to view comments. Keeping the comments on a separate page is particularly nice, because often on YouTube you'll find distracting or offensive comments and being able to bypass them entirely makes for a better video-viewing experience. But if you want to get in on the discussion, it's still only a tap away.
What makes Jasmine a joy to use, even above the original YouTube app, are the extra features and the overall feel of the interface, but it's worth noting that the app is constrained by YouTube's policies. In the most recent update, for example, Jasmine had to remove customizable skip and rewind controls and automatic background audio playback, and had to add 2 seconds of video load time to make regular playback YouTube-compliant.
Jasmine added several new features in the same update. You can set a preferred playback quality in the settings, make Watch Later lists in the playlists section, and view a new My Videos section for those who create videos regularly. Even with the constraints from YouTube, the active development of the app promises even more features in future updates, so I think the positives of this app outweigh the negatives.
Overall, Jasmine makes it very enjoyable to browse, search for, and watch videos on YouTube. It has customization options, a great-looking and logical user interface, and plenty of more features promised on the horizon. If you like watching YouTube videos, Jasmine is one of the best ways to do it on an iOS device.