The two Twitter clients I use are Tweetbot 4 and the official Twitter iOS client.
Reasons for using the official client over Tweetbot:
Better location tagging, using Foursquare data. (Why doesn't Swarm post the exact location to auto-tweets?)
Twitter Cards are enabled for all domains, not just approved publications/apps. So your blog shows a preview if you've set it up right. Come on, Facebook/Instagram, join the party!
I wish Twitter had something like Facebook's Instant Articles.
You can see pinned tweets, and Twitter threads in context.
Search works back to day 1. Tweetbot 4 only searches back 5 days or so. The Twitter iOS app is your best bet for checking if someone made the same joke you're about to make.
Native muting, which syncs to the Twitter website.
Reasons for using Tweetbot 4 over the official iOS client
Muting by keyword, regular expression, and based on app, which syncs across Mac and iPad.
It shows Instagram previews, whereas Twitter doesn't.
Options for avatar display (circle or square) and whether verified badges show.