What is the best/fastest way to copy tables?

[Wim Roffel]

I want to copy the data section of some software into an installation of a newer version of that software. That means that I have the following requirements:
- not all the tables should be copied, only about half of them.
- the tables into which the content is copied have the same names as the old tables. However, there are minor differences: some fields have become wider and some fields have been added. It is desirable to initiate these new fields as empty instead of null.
- occasionally it may happen that some extra restriction - like some extra unique key - has been added. It is no problem when that ends the process. However, it is desirable that the error message is clear.

I want to do this from PHP code and was wondering what is the fastest way to do this. The transfer concerns about 150 tables that in total contain a few million records.