Bye going from the fat to the slim version here are the.
Advantages.
1. Its smaller hence the word slim.
2. Its lighter.
3. Larger hdd and upgradeable.
4. No piano finish which makes dust and fingerprints not seeable.
5. No bulky power cable so it doesn't look like a rope.
6. it runs more quite.
7. If you ask me it looks sexier.
8. Physical power and eject button with instant action.
9. Since its small it will save you real space.
Disadvantages.
1. No backwards compatibility.
Note:
Yes the hardware is the same also if you buy one make sure to use the data transfer utility that way you can transfer everything from your fat to the slim, check the link below on how to.