As long as you plan the migration and execute it properly, it will look the same.

Here's some food for thought, though:

• Managing your own server means you're responsible for security of your server and site
• As this is a Linux-only hosting, you will need to either have someone with Linux knowledge, or learn it yourself.
• There a TON of how-tos here, so if you get lost, I'd say look at the tutorials for the answers you'll need
• If the answers you need aren't there, we will help you here, if possible.

If this seems like too much, self-hosting may not be the best answer for you.