Most Helpful Guy
You can use either to achieve what you mentioned, so it's up to you and your preference. Sony Vegas probably would be better for you. However you can't really compare After Effects and Vegas Pro. Vegas Pro is video editing software and After Effects is special effects and motion graphics software. Comparing these is like comparing Word and PowerPoint. Adobe Premiere is equivalent to Vegas Pro. That being said, Vegas Pro does have some special effects features so for some it's simpler to use just that instead of Premiere and After Effects combination.
Personally I prefer software from Adobe but Vegas Pro isn't bad at all either.
Most Helpful Girl
After Effects. I would die for Vegas but after effects is... Well for effects. It'll more compactly so what you need.