After Effects preview lagging but Premiere pro preview runs fine

After Effects is not an NLE, it is a visual effects, animation, and compositing app designed to create shots you cannot create in an NLE like Premiere Pro.  NLEs use a completely different system to run previews.

Preview performance depends on the composition frame size, frame rate, Comp Panel resolution, and system resources. After Effects looks at every pixel on every layer for every frame, loads those pixels into memory, figures out what you want to do with them, then caches a frame and moves to the next one. NLE's playback an automatically scaled to the size of the monitor panel video stream the same way that a media player like the one your browser uses to playback YouTube videos does. Modern systems can playback two or three movies in real-time fairly easily because they don't use many resources. 3D apps and visual effects apps line AE use an entirely different workflow. You must adjust your expectations and manage your projects to get reasonable playback performance in AE. It is a lot better than it was a year ago if your system is properly set up and compatible drivers are in place. Some builds of AE have problems with some systems, and is is often a good idea to roll back a build or a version when you have issues than it is to keep fighting your configuration. 

Give us system, footage, workflow, and software version details, and we may be able to help you improve your system's performance. If you are new to AE and visual effects production, be prepared for a steep learning curve and spend some time with the User Guide and in the Learn Workspace or utilize the Home Screen to figure out the UI and the basic workflow. Pay attention to the fact that every tutorial in the user guide and the learning resources for AE show you one shot compositions. None of them try to edit a movie.

Have you tried going to edit/purge memory and disk cache and seeing if that helps?

Without any system info and critical details like hardware acceleration settings, cache setting, preview settings and so on we can tell you nothing. You need to be much, much more specific.

Mylenium