AIFF and Apple Lossless are audio formats that do not reduce the amount of information in data, and that is why they can be termed as non-lossy formats. There cannot be any loss of information whatsoever when you are converting between non-lossy formats. They are both good as they perform almost the same function.
However, there are some differences between the two formats. AIFF format does not support compression, meaning it can't be compressed, while Apple lossless supports compression. This means audio with apple format can be compressed to have more space on the disk, or to reduce its size.
It should be noted that when you compress audio with apple format, it doesn't reduce its contents. As a result of compression, apple lossless files are relatively smaller than AIFF lossless files. Another difference is that; Apple lossless files do not drain battery compared to the level at which AIFF files drain the battery.