In fact, both AIFF and WAV are lossless audio file formats that contain uncompressed PCM audio data. In terms of file size and quality, the two formats are essentially identical. Both of them are keeping CD quality and occupy a lot of storage space. The biggest difference is that WAV is an old popular format developed by Microsoft & IBM and is pretty much universal for most devices.
On the other hand, AIFF is regarded as Apple's equivalent to WAV. As a result, AIFF is more widely-used in Apple products. If you use Apple devices and prefer uncompressed RAW files for post-production, AIFF is the better option. If better compatibility and flexibility across multiple platforms is your priority, there is no doubt that WAV is better for you.
Besides AIFF vs WAV, you may be also interested in: AIFF vs FLAC.