There are scientific studies that prove that MP3s above 256 kbit/s and AACs above 192 kbit/s are not distinguishable from the originals even with good audio equipment.
If a human ear can't distinguish the original from the compressed file, I don't care for the parts that were left out, so I don't deem lossless compression particularly useful except for archival purposes (remastering might have use for inaudible details).
As a side note, even the data on a CD is lossy: the 16 bit quantization means that any dynamic peaks over 100 dB can't be stored (the human ear can hear up to 120 dB) and the sample rate of 44.1 kHz means that any frequency above 22050 Hz can't be stored (the human ear can hear up to about 20 kHz (children) or 16 kHz (adults)) and anything above about 20 kHz is severely distorted by the aliasing-filter used in mastering. However, the limitations of the audio gear are usually far greater than the limitations of the format.
Technically, AACs are MP4 files. MP4 is the official successor to MP3, which sports better audio quality at the same bitrate or the same audio quality at lower bitrates. All lossy audio formats look for masking effects (you don't hear background details when the foreground is loud) and compress masked frequency/time-blocks. Usually, compression is done by downsampling (MP3/MP4) and quantization (MP4). Additionally, the file is entropy-encoded (basic file compression). The achieved audio quality is basically dependent on the masking detection algorithm (this is were LAME improved MP3). The file size is dependent on the compression method (this is were MP4 improves MP3).
Hence, I use AAC with 256 kbit/s just to be save. If you insist on using MP3 for compatibility reasons, you could step up to 320 kbit/s. Note that with some players, playback of MP3s uses less battery than playback of AACs.