You have full control on a dedicated server. If you have server administrators, they will definitely suggest you to go for dedicated server. Keep it in mind that VPS is still shared.
Dedicated server is a standalone server. It maximize performance. Security is a different topic and it needs to set up on both case. Whether or not it is safe enough, it depends on your security policies.
Yes. You will have full control on a dedicated server.
No, they are same.
It was very smooth when I switched to VPS. However, some customer did have some problems during migration. I'll say it's better to make a decision now than later.