It can be better, it can be worse, it can be identical.
Better if your original was worn or just not pressed well, and with a good ripper and burner hardware/software you produce a better copy. How is this possible? Because a ripper is not constricted to real-time audio performance and will take all the time alloted to it to extract the bits and perform necessariy error correction.
Worse if you don't have ideal burner, software, hardware, and the original copy happened to be good. Or your player happens to have a hard time with the CDR media in question.
Identical if the transport you happen to use for audio also takes the time to buffer and re-read the audio at faster than 1x. Notice that most home audio players besides Meridians do not do this. PCDP's with anti-shock mechanisms do this, wheter or not the buffer quality and mechanism produces extremely low jitter is debatable. Winamp + CD reader plugin may do this, but unless you have a very quiet computer, with an exceptional pro-audio card and DAC, the advantages will not really show through since the computer environment itself is mechanically and electrically noisy, and induces jitter more than average home audio players in the first place.
Digital is digital, however CD's are not *exactly* digital...they are analog media in the sense that pits are analog...it is the conversion of the spacing of analog pits into discrete values that is digital. It is during this conversion process where differences may present themselves although slight. So a CD doesn't really contain discrete values...it contains pits which are converted into digital. If these pits are allowed to be re-read until the resultant data is transcribed correctly, than it is identical. If they are read only once...than the transcription is not guaranteed to be bit perfect. Analog is anything in the real world, digital is an abstraction of analog for the purpose of reliability, and duplication or manipulation of data. The CD only becomes a digital entity when read by a transport which could be considered an Analog -> Digital stage, although probably a very reliable and robust one. Without the transport, it is just a disc with spaced out pits, and hence analog in nature. Transports are not always perfection. Course the whole point of digital is in fact to remove distortions of analog nature, but we are also talking about a real-time non mission-critical application. Again if you are using winamp + CD-reader you are telling your system that you don't want it read once...you want to utilize system memory as a large buffer, and you want it read to the best ability and most redundancy you can offer. If you believe the CD-reader plugin offers you better performance than other digital CD-readers, than digital isn't really just digital anymore is it.
If you have an extremely fast CDROM you may notice some CD's or CDR's spin and read faster than others...while others apparently induce enough errors to tell the CDROM, "hey I'm getting too many read errors, slow down please". Because of computer technology, people get spoiled by how much is done behind the scenes that they tend to think things are either perfect, or broken, but there definitely is a grey area. These error messages aren't going to flash up on your OS, they are part of the OS and CDrom drivers and firmware.
Also did you know most hard drives are not bit perfect devices that are *exactly* digital. There is a level of performance provided by magnetic media which although very high, is not bit perfect...and as such hard drives automatically will contain more space than specified and although there are probably non-read/writable areas on the harddrive it will automatically use the extra space without you knowing. This is called defect management and is entirely different from "bad sectors" which is on the operating system level, not hardware level. If you see bad sectors reported from the OS, its probably because it had difficulty reading and writing, and basically performs defect management on its on (hence low-level formats can remove bad sectors...but if a hard drive is just bad, those bad sectors will probably come back). Again hard-drives are not always just perfect, or broken, but definitely have grey areas of performance and reliability as well. Same as CD's.
You can go out and buy hard-drives and think only of speed, GB's, and price...but those that know better know about quality.