Exactly as Steenamaroo says. The cable and connectors make no difference at all to the sound quality. Both (assuming the quarter inch is a TRS one--that's "Tip/Ring/Sleeve") carry balanced audio signals.
However, there are conventions as to what things are used for. On a mixer or audio interface, an XLR connector generally means a microphone input while a quarter inch jack normally carries a line level or instrument level signal. This is important because a line level signal is vastly louder than a mic signal--a difference of 40-60dB typically. This means that, if you use an XLR to jack adaptor cable and plug your mic into the jack socket, it will be so quiet you'll be lucky to hear anything. Conversely, plugging a line signal into a mic input will likely overload it and result in totally distorted sound.
So...although there's no difference in the cable/connector quality, there can be big differences in function.
