How much Unity iOS Pro license affects on application size and loading speed?

How much application size decreasing with iOS Pro license? Is there precise amount of megabytes or percent of the application?

And also is it increases speed of assets loading or only phase where Unity logo appears?

There is no set amount that will be stripped. You can expect several megabytes (an empty Unity app will be stripped from 13 to ~6 mb) usually, but it is based on what namespaces you include and what you reference.

Don't reference more than you have to and avoid System.Xml especially.

It will decrease load times initially because simply there is less to load, meaning a shorter time for the Unity logo (which you can change since you have the Advanced version I would like to remind you). :)