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The big advantage of a digital recording system is that it is tolerant of faults to a large degree. As long as the strain on the system isnt too great, any problems will be eliminated completely and a recording will play back 100% perfectly. Many of the analogue problems are no longer troublesome:
NOISE. Modern metal particle tapes allow recording to be done at a very high density. Getting more information onto the tape means that in proportion the DISinformation - the noise - will be less. In a 16 bit digital system the signal can be resolved so finely that the noise is at a level 96 decibels below the loudest signal. In a cassette, this figure is more like 55dB, even with noise reduction.
FREQUENCY RESPONSE. The tape in a Compact Cassette travels very slowly past the heads. Since high frequencies have very short wavelengths it follows that it is difficult to squeeze them onto the tape in the space available, and difficult to play them back too. In the DAT system, the tape moves even more slowly, but the head is also in motion to compensate. In a Compact Cassette recorder, the relative speed between tape and tape head is 4.75 centimetres per second. In DAT it is over 3 METRES per second.
DISTORTION. In a digital system, noise and distortion go hand in hand, therefore if the noise is low, then the distortion is low too, all the way up to peak level. Compact Cassette suffers from the normal amounts of harmonic and intermodulation distortion at reasonable recording levels, but when high recording levels are used to bring the signal up above the noise floor, then distortion increases.
WOW AND FLUTTER. If a Compact Cassette recorder is new or particularly well preserved, then wow and flutter can be kept to reasonable amounts. But there seems to be no limit to how bad things can get, particular in car and personal stereos. In a digital system, the data may be read off the tape at an uneven rate, but it goes through a digital buffer where it can be read out at a constant speed, no matter what.
Of course, the Compact Cassette must have some good points or it wouldnt have become so popular. The first and most obvious benefit is that it is so incredibly cheap. Cost will be a very big hurdle for any digital system to jump if it is to compete. Compact Cassettes are also very er... compact, for want of a better word. And the players they go into can be little bigger than the cassette itself. Acceptance of DAT in home hifi would probably come relatively easily if the domestic setting was the only consideration, but since personal stereos are so important, DAT will have to compete in that arena too. If DAT cant win the whole game, then I very much doubt that it will enter into the lives of many people at all.