No school can take you all the way to an ATPL. For issue of that licence you must have at least 1500 hours flight time, of which at least 500 hours must have been in a multi-crew aeroplane. Whichever route you take, you will end up with a CPL/IR and the ATPL theoretical knowledge exams.
As to the advantages/disadvantages of each route, the following spring immediately to mind but there are doubtless others:
Integrated
Intense, structured training usually means that you can reach the required standard in less hours
Aircraft are often (not always) more plentiful, better maintained and show commonality of instrument and avionics fit.
Instructors are usually (not always) more experienced, better trained and standardised, better paid and more highly motivated towards the needs of the student.
There are no minimum hours required to commence the course
You only need 150 hours of flight time for CPL issue.
The course includes everything you need to get into the right hand seat of a multi-crew aeroplane
It's expensive!
Modular (PPL-ATPL Theory-CPL-MEP-IR-MCC)
You are not committed to a 12-18 month chunk out of your life, you can do the training in easy stages.
You are not committed to one school for all of your training but can mix and match training providers, completing each module at a different school.
Some (the minority) of the training providers are less than scrupulous in their dealings with students - don't commit too much cash 'up front'
You must hold a PPL and have completed 150 hours of flight time before commencing the CPL course.
You need 200 hours of flight time for CPL issue.
You must complete the theoretical knowledge training within 18 months and apply for issue of the CPL and IR within 18 months of passing the last exam (this is guaranteed in the case of integrated training).
It's cheaper!
Note that the ATPL theoretical knowledge exams are necessary in order to add a multi-crew aeroplane type rating to your CPL which, in turn, is necessary if you are to achieve the 500 hours multi-crew time necessary for ATPL issue.
Note also that no US school is currently approved to provide ATPL theoretical knowledge training. They may have an 'agreement' with a school in the UK to provide this training and may pressure you to use that school. You are, however, free to choose any training provider you wish for this module.
The only schools currently approved for ATPL theoretical knowledge training are:
Atlantic Flight Training - Coventry ( Distance Learning only ) (Residential in South Africa); Aviation Training Associates (Residential); Bristol Ground School (Distance-Learning only); Cabair College of Air Training (Residential only); Four Forces Aviation ( Distance Learning only); Glasgow College of Nautical Studies; London Guildhall University (Residential); Oxford Air Training School; Professional Pilot Study Centre; SFT Aviation Limited.