Difference between FLAC and others like MP3 or WAV?

Just wanting to see why FLAC is more preferred than the other audio formats. Thanks in advance.

flac lossless (same quality for as CD or source)
wav lossless also, but size 2x MB
mp3 smaller, but losing quality to make small. not notice bad headphones/speakers for cellphone, but computer speakers good, noticing.

By my experience – FLAC is truly lossless, but WAV from the same FLAC may sound definitely better. I understood that it depends from realisation of your player. Computer players have different engines and algoritmes and may sound different. Hardware players have different decoding chips , various levels and costs. Once I had Sony blue-ray player. I discovered that it played WAVs much better than FLACs, so I converted them. Pioneer car-player, if it supports WAV may sound better on it. I have separate respected DAC (M-DAC Audiolab) at home and differences were clear. You may not hear differences with simple player. You should listen by yourself.
In any case – mp3 is waisting of space and time.