When I started learning Python, I created a few applications just using functions and procedural code. However, now I know classes and realized that the code can be much readable (and subjectively easier to understand) if I rewrite it with classes.
How much slower the equivalent classes may get compared to the functions in general? Will the initializer, methods in the classes make any considerable difference in speed?
No.
In general you will not notice any difference in performance based on using classes or not. The different code structures implied may mean that one is faster than the other, but it's impossible to say which.
Always write code to be read, then if, and only if, it's not fast enough make it faster. Remember: Premature optimization is the root of all evil.