I use the TDK headphones for few weeks already and can't complain about them. In fact I'm very happy not to be wired with the detector. I do not notice any lag, the targets are usually, where the detector reports them
The volume can be set on the headphones separately, so no issue there. I go out almost exclusively for coin shooting (predecimals) with my X-Terra, so I can't say much how the sound is when hunting for gold (in prospecting mode). For me, the sound is excellent for my purposes, I wouldn't expect anything else if in prospecting mode.
You just always need to keep a spare set of batteries close enough. It lasts quite long (I would say 10-15 hours minimum), but you never want to be disturbed by such issues.
You have to be always carefull with the transmitter, it's all plastic and if you accidentally drop the detector, it could break easily. And the plastic battery cover on the transmitter could be quite easily lost, so it' better to fix it with some tape (or if you have any other idea). This headphones are not primarily intended to be used for this purpose.
Otherwise I'm very happy with the purchase