It really is personal preference and just what you would be doing, Adobe After Effects is a pretty complex tool, and you will need to look at lots of tutorials just to do some basic things, Final Cut is not the same thing as After Effects, Final Cut is an actual movie maker, whereas After Effects is strictly to make effects, and then wants you to buy Premiere Pro for the movie making itself, Adobe After Effects has more effect capabilities than Final Cut, but can't really make a movie as easily. Personally i use Adobe After Effects and Premiere Pro, they are very good products together. A lot stronger than Final Cut.
Another view:
Final Cut Pro comes as part of the Final Cut Studio package which includes Motion (See links below) which is the equivalent of After Effects. Many professional producers use the Final Cut Studio software.
Final Cut Pro is the best editing system and for effects is Adobe After Effects.
EZTiltles,MacCaption & CaptionMaker, Subtitle Edit,Aegisub,Adobe Premiere Pro,Adobe After Effects,Final Cut Pro, Adobe Audition
they use final cut pro/express for video editing and adobe after effects for special effects
You can't. Final Cut and After Effects have their own proprietary file types. It only works with After Effects and Premiere because the were both created by the same company and specifically designed to be compatible.
Final Cut Pro and Adobe After Effects IMPROVED: Editing: Final Cut Pro 7 Effects/Compositing: Adobe After Effects CS4 Color Correction: Apple Color Music: Apple Logic Pro Sound: Pro Tools 8 with an Mbox 2 3D Elements (Jedi Mailboxes, e.g.) - 3DS Max Copied from Freddiew.
Many effects will work in both FCE and FCP but not all of them will.
Sony Vegas Final Cut Pro Adobe Premeire Pro CS5 Adobe After Effects Adobe Photoshop Pinnacle Studio VideoPad Video Editor I'm sure there is alot more, but just a few to name. VideoPad is the cheapest, at $30
The latest model of Mac Mini (2011) will work for Final Cut Pro X, but it will be noticeably slower to add and render effects etc. An iMac would be a better option.
Final Cut Pro
For Mac: Final Cut Pro 7 or Avid Media Composer. For PC: Adobe Premiere or the complete Adobe Creative Suite.
You use Adobe Premiere to create movies, edit videos, etc. Adobe Premiere is like a more professional version of iMovie, Windows Media Player, and is closely related to Final Cut.
Alternatives to Final Cut Pro include Avid's Media Composer and Adobe's Premiere (See links below).