STOP-MOTION IS JUST CLAYMATION, RIGHT?
Well, yes... and no. Stopmotion can be claymation, but it can also be many other things. Stop-motion is simply the process of taking inanimate objects, moving them a small amount and taking a picture. Do this over and over to shoot 24 frames for every second of animation. It is very similar to cel-based animation but it takes place in the physical, 3 dimensional world. You can do stop-motion animation with puppets and miniatures, objects like garden tools or chairs, or even people.
COMPUTER GRAPHICS ARE EASIER
We cheated; this is actually a lot like question 1. The fact is CG can sometimes be easier, but not always. Confused yet? Okay, so think about creating a photo realistic potato chip in computer graphics. Designing, texturing and lighting that chip would take days. How long does it take to get a real potato chip? Open a bag. The point is it depends on what you're shooting. If you want to do a quick animation of some tools moving around and forming a word stop-motion is much faster and less expensive. Want to do an environment with a lot of buildings and huge outdoor landscapes? CG might be your least expensive bet.
CG LOOKS BETTER
Okay, let's talk about look. Stop-motion is physical, it's real. That handmade look comes through on camera. CG artists strive to capture that look (at great expense). The Lego Movie mapped fingerprints onto the Lego blocks used in the movie to try and recreate that look as much as possible. Every toothpaste or insurance commercial, kids cartoon and (yes) blockbuster film uses CG. It's now become a 'common' look. It's expected. If you really want to stand out you should do something different than everyone else. Stop-motion is definitely different.