Assuming that you can afford both options, then the question comes down to one of what form of study best suits you. Some people thrive on self study and some find it impossible.
Although a great many people pass their ATPL exams through self study, many others do not. A very small minority of those who pass their exams each month announce it on this forum. Approximately 150 students took the September exams. The average pass rate for the 14 subjects was something like 80%. Even the most pesimistic estimate would suggest that at least 100 people passed most of their exams. Now compare this with the number who posted on this forum to announce their success.
But those who either drop out, fail their exams, or decide to switch to full time will rarely if ever want to tell everyone about it. Don't allow yourself to be fooled into thinking that the good news that appears in this forum is the only news.
This post is not intended to be a dig at BGS nor at any other school. A very large proportion of BGS students pass their exams. But I have taught other students who having failed to pass their exams through self study (at BGS and others schools) have switched to full time study and subsequently passed the exams at the next attempt. To be fair to BGS, I should also state that one such student came to me having had problems with the full time course at NAC.
At the end of the day you must judge which method and which school is likely to best meet your needs.