I have an iPhone 4 running iOS 6.1.3. I primarily use it as an iPod Touch gym music player after retiring it for the iPhone 5.
After using the iPhone 5, the limitations are very apparent. Buying a new iPhone 4 means it will likely ship with at least iOS6 - the transition to iOS 6 has not been very kind to the iPhone 4.
Safari is passable in normal browsing, but when viewing pages with lots of image and HTML5 content, the browser slows to a crawl. Even simple animated gifs choke up the iPhone 4 when scrolling/typing on a webpage. Lots of checkerboarding when scrolling, and the 512MB ram gets eaten up fairly quickly after a few open tabs.
Speaking of the ram, cached apps go through the memory very quickly. Many apps in their suspended state will be restarted after a little bit of inactivity.
The keyboard responsiveness is also lacking. If you type too fast, the keyboard will freeze and hang on one letter before catching up.
The iPhone 4 can still handle many of the graphics intensive games available on the App Store, but at reduced/choppy framerates.
If you're happy with just basic functions, like light browsing, music, email and messaging - it works. But at this point, the A4 is very underpowered for the amount of pixels it needs to push. It wasn't so apparent with iOS4, but it really shows its age now.