Two MySQL requests at the same time - Performance issue
It looks like 'page swapping' is the problem here. 

When you deal with one table at a time, its indexes and parts of the table are loaded into the RAM. If you keep dealing with the same table, it will be fast as the table already exists in the ram.

On the other hand, if you keep changing the table that you are dealing with, then the data in RAM has to be written to the disk, and the second table's info will be loaded to RAM. This is one of the MOST EXPENSIVE operations.

Solutions!! Not straight forward though: You may distribute your DB, or run your scripts sequentially. Hardware upgrade may make the process faster.