DCS uses a rotating series of codes like 257257257257 which in this case is 257 repeated continually. CTCSS uses a sub audible single tone like say 100 hz. Once a CTCSS squelch is open, wide band noise like intermod or computer hash can keep the squelch open after the transmitted carrier when its sub audible tone stops, resulting in unwanted noise at the receiver. Sometimes the noise can have enough of the required sub audible tone to open the squelch and keep it open, resulting in jammed repeaters etc.
However with DCS when the rotating code stops, the squelch can not be kept open by outside interference. Also at the end of the transmission the transmitting radio sends a "close squelch" command which causes the receiving radio to close its squelch before the transmitting radio ceases its transmission. This eliminates the common squelch tail resulting in a much cleaner end of transmission. The voice just stops without any noise or tail.
DCS works much better in urban high noise environments and in my opinion produces a much nicer "sound environment". There is voice, then no voice, without the CTCSS hiss and crash at the end.
The 3 digit rotating code like 257 means that code 572 and 725 will give the same 57257257257 sequence so only some of the codes are listed. If 257 is the code, then although 725 and 572 will generate the same sequence the listed 257 should be used so as not to confuse the user into thinking they are distinct codes.
Try it on simplex. Set up two memories on the same frequency. One with CTCSS and one with DCS. Then have both operators change together between the memories and do a "side by side" comparison. I have been using DCS on repeaters and simplex for years and really like it.