Twitter has created a fair amount of controversy by being aggressive in either developing their own or purchasing third party mobile Twitter apps. Ironically, Twitter started by first developing mobile and desktop web apps, and frankly I primarily use the desktop web app to access Twitter from my personal computers. The mobile web app has also been pretty good, but hasn’t had many of the features you find in mobile Twitter apps, however, Twitter has announced that they are rolling out a new version of the mobile Twitter web app that adds some of those features.
The new mobile Twitter web app is built using HTML5, which enables it to look and act like a full application. You access the site by simply entering twitter.com in Mobile Safari on an iOS device, or the Browser on Android devices. In the screenshot you see a comparison of the old mobile web app on the left, and the new mobile web app on the right. Twitter is slowly rolling out the changes to users, so you might not see it right away on your phone.
If your phone is running low on storage space, one way you can free up space is by uninstalling apps like Twitter for which there is an equivalent web app and simply use the web app. It looks like the changes Twitter has made makes the shift from a full app to a web app much less drastic.