The type of musical information that gets lost when encoding to a lossy format is actually quite dependent on the genre (or, more accurately, the type of sound being represented). Rock music and its variants tend to give more complex waveforms, having more harmonics due to the relative dominance of distorted or percussive sounds instead of the more "pure" sounds of classical music. When there aren't enough unused bits in the stream to allocate to representing this information, the encoder has to throw some of it away, and the results can sometimes sound pretty bad (Big example: cymbals).
Contrastingly, classical music tends to be much more complex dynamically; that is, on the amplitude spectrum rather than the frequency spectrum. You need a lot of bits to be able to represent the broad, expressive changes in dynamics that may be present, and sometimes this data cannot fully fit into the bitstream, and must be thrown away.
Also, classical music can lose some of its "crispness", because "crisp" sounds are harmonically rich data that sometimes gets thrown away from the lossy bitstream just like the cymbals in a rock recording, although the dynamic range loss is usually a more primary concern.
With all that being said, I am a believer in lossy formats when it comes to recreational music listening, but I think it is very much up to personal preference. I prefer to fill up media drives with five times as much musical content for the token loss in content than insist on always listening to a perfect representation. If I strain my ears I can sometimes here a difference between high quality MP3s (like 256, 320kbps) and a lossless version, but at high bitrates, it's never been an obstacle getting in the way of my enjoyment of the music. Think of an old, early audio recording that emotionally moves you. Your mind's ear can hear past the poor quality and discern the musical expression even through the fuzz, and these quality losses are much more severe than those of a high-bitrate modern lossy digital format.
So, I say professionally, always retain all the data you can and store your audio lossless, but when it comes to your own recreation, just go with a decent lossy format until you find that it's keeping you from enjoying the music itself. (And keep a lossless backup if you're worried, either the original physical media or some big hard drive).