Option 1: Bluetooth audio.
Option 2: 3.5mm TRS analog audio connector (wired).
Facts about Bluetooth:
- Bluetooth audio protocol is lossy, meaning that some of the data is lost. However, it is digital, meaning that the audio reproduction in the headset is bit-exact the same data that was transmitted.
- The data is encoded to a digital format that is compressed in a way that loses some of the source data (but hopefully not enough that you can perceive it); but the data stream is much more resilient to interruption, due to buffering, which means that you are unlikely to notice even if some other electromagnetic frequency transmission interferes with your bluetooth (temporarily).
- See A2DP at Wikipedia for more information about Bluetooth audio. To put it simply, there are more than one supported audio codec, and they have varying pros and cons in terms of bandwidth consumed, energy consumed, compatibility across devices, and quality. Some of the newer codecs such as apt-X produce what many consider to be superior audio quality, but device support is limited compared to the older codecs, or SBC which is required by the A2DP standard.
Facts about analog audio:
- Analog audio over a standard 3.5mm headphone jack (technically called a "TRS" connector) can be very high quality if the audio playback device has a good DAC. An amplifier (separate or built-in) can make the signal sound even better.
- A "good pair of cans" (good headphones) can sound amazing with this dated analog mode of transmitting audio down a cable. If you are using a very high quality DAC on the source audio device, chances are it's better than the DAC that has to be in the bluetooth headphones to convert the bluetooth digital data to analog, because the in-headphones DAC is limited by battery power and size constraints -- but a sound card in a computer is much less constrained. Even sound chips in smartphones are great these days.
- All analog audio is subject to interference with the audio cable. Most audio cables are not shielded from external electromagnetic interference, and certain models of computers (especially Core 2 Duo era CPUs with on-board graphics) have been known to spew electromagnetic frequencies that are picked up as a "grinding" or "buzzing" noise on the analog headphone wire, if it is near enough to the computer. Some LCDs can do the same. Depending on your situation, this interference can be even worse than the loss of audio quality of bluetooth's lossy encoding.
The answer is that it heavily depends on your situation, and exactly how sensitive your headphones are, and exactly how good the Digital-Analog Converter (DAC) in the bluetooth headset is, and which codecs the bluetooth headset supports, and........ (many other things). If you're using the headphones in a way that a wire would get near certain models of LCD or computers, the analog signal quality may be terrible due to interference. If you're using the bluetooth in a way that it's in a heavily saturated 2.4 GHz environment (e.g. lots of WiFi signals, microwaves, cordless phones around), it may drop out due to heavy interference and crosstalk. Also you have to be able to live with the quality loss of lossy encoding for one of the bluetooth A2DP codecs, if you go that route. You probably can't detect it if you listen to lossy audio vs. lossless, but some people like to fake themselves out and say that they can tell ;)