Fat grafting to breasts
is certainly more widely accepted now and with a few years of experience, it appears that it is safe but no one can guarantee that. It isn't dangerous to your well being and it does take more then one session to achieve the results that most want. But if you go overseas and have complications, you will be paying more out of pocket to have it managed in your country so its always best to stay local.
Fat transfer breast augmentation
Fat transfer may be natural and sound like a good idea, there are many problems with it:
1. only one cup size can be achieved
2. some of the re-injected fat calcifies, which could be mistaken for breast cancer on a mammogram.
3. you may develop oil cysts and tissue scarring
4. results can be unpredictable and require many sessions to achieve your desired results.
Currently, there is no research that proves fat transfer is safer than implants (silicone or saline).