Great Article listing all the facts :
Integrated vs. Modular ? Which route to take | The Student Pilot Blog
to sum it up. Both integrated and modular will give you the same end result:
An EASA frozen ATPL (no difference - no comments on you license). The only way to tell the difference is on your CV or during the interview.
So, the only difference between the 2 is the course structure.
Integrated = full time course, more intense course with one only FTO.
Some of the training might be done abroad ie.: USA. This is the norm for the hour building part.
Modular = "A building block" course. You can pick and choose between the FTO's. Ie PPL with Oxford, hour building in the USA, IR with Atlantic and so on. It allows you to change FTO should you not like the place / instruction given and it allows you to "save" a bit of money as well, as FTO's are competing for your business.
- I would probably recommend you to do the IR in the UK. If you want to save money do it on the hour building part or CPL part of your modular course.
Good luck!!