Statistics prove that 80% of low hours (fATPL) pilots recruited by the airlines are those who have completed their training via the modular route. (BA being the exception)
As already mention most airlines insist on no more than 2 training providers if undertaking modular training.
As far the distance learning ATPL verses full time ATPL, I would think that a first time pass and good results are more important to the airlines than what method! It takes a lot more discipline & motivation to study at home rather than in a class room setting!