exporting into Final Cut Pro or premier

After Effects is for creating effects, animations and graphics you cannot create in an NLE. If the comp is simple you can use Dynamic Link to drop any comp in a Premiere Pro timeline, but you will have to render to a visually lossless production format like ProRez to use the footage you create in AE in Final Cut Pro. 

I never use Dynamic Link in Premiere Pro on a comp that takes a long time to render. By a long time I mean longer than a few frames a second because Dynamic Link will open up a background copy of After Effects to do the rendering and that render always takes longer. Sometimes it takes a lot longer. A lot of my visual effects comps take sevral seconds a frame to render, some over a minute a frame, and those comps would bring Premiere Pro to it's knees, it would take as long to render a preview in Premiere Pro as it would to render a proxy file in After Effects, and the final render could be in jeapordy if the background copy of After Effects chokes on the comp.

I hope this helps. Remember, AE is NOT a video editing app and it is not intended to be. The only reason you should ever have more than one shot in a comp is that you need to do a transition between shots that you cannot do in your NLE.