Unserialize can't store data. Unserialize is a function. Unserialize converts data from serialized form. It then stores that output in a variable in PHP. So technically, this isn't a storage system, but an interpretation construct.
Include can only store static data that can be difficult to update.
Databases are fast, and efficient when dealing with data of all types. Depending upon the table type (InnoDB, MyISAM, etc.), table structure, indexing options, (etc.) can help or hinder your speed.
Let's put it this way:
Unserialize
It can serialize what you need into one variable, but that variable value needs to be transferred via Session, Cookie, or hidden form to progress from page to page. No long term storage.
Include
Is good for things like config files, and general function keeping. Depending upon the includes, how big the file is, and what computation is needed can slow down your program (or speed it up in some cases). Pretty long term storage. Can be accidentally modified.
Database
A database is meant to move, store, and update data. It's easy to work with, efficient at what it does, and constantly improving. If you're storing things like posts, comments, photo information, letters, blogs (etc., etc.) then this is the way to go. Harder to accidentally modify parts, easy to mess up the entire system. Much more robust than any other data storage technique I've seen.
Really, what it comes down to is your needs. What do you need? What are you going to be using it for. Each has its own advantage and disadvantage in certain situations. In answer to your question: No, none are inherently slower. But that depends on many things like server speed, time of day, work-load at that specific moment. There are other factors that really go into speed. So what you should be asking is: Which of the three would be better suited for __________? That's a question that can be better answered.
