Ok, so like user22766 was saying, it might have to do with being balanced or unbalanced. If that adapter is unbalanced (using a TS connection) then you may pick up noise there. I assume the adapter is short though, so that shouldn't make too much of a difference. Unbalanced signal is fine if you keep it short.

Another cause could just be that you are creating more connection points. Each time you 'plug in' to something, that connection point will lose a bit of signal strength. So adding in the adapter gives you one more point of signal loss. I again feel like this wouldn't make too noticeable of a difference. Perhaps this issue combined with the last could create the difference you are noticing.

Now lastly, you say there isn't a preamp? This is not good, and will negatively affect your sound for sure (making it sound lower in volume and not as deep in the low end, just like you described). That doesn't answer the DIFFERENCE between the two signals though. Are you plugging in to the same input when using the adapter? If that's the case, then the preamp would not be the problem.

It would be helpful if you told us the name of the mixer, as that (to me) seems like the most crucial piece to this problem.

Ok, so like user22766 was saying, it might have to do with being balanced or unbalanced. If that adapter is unbalanced (using a TS connection) then you may pick up noise there. I assume the adapter is short though, so that shouldn't make too much of a difference. Unbalanced signal is fine if you keep it short.

For reference, this is a balanced 1/4" connection (TRS) Notice the two black lines. The first section of metal is the sleeve, then between the lines is the ring, and finally the point is called the tip. These are three separate signal paths.

Here is an unbalanced 1/4" connection (TS) on top. (The bottom is a 3.5mm connection) Notice the ring is not there anymore, leaving only two signal paths. This doesn't allow the noise rejection possible with the TRS cable.

Now, another cause could just be that you are creating more connection points. Each time you 'plug in' to something, that connection point will lose a bit of signal strength. So adding in the adapter gives you one more point of signal loss. I again feel like this wouldn't make too noticeable of a difference. Perhaps this issue combined with the last could create the difference you are noticing.

Now lastly, you say there isn't a preamp? This is not good, and will negatively affect your sound for sure (making it sound lower in volume and not as deep in the low end, just like you described). That doesn't answer the DIFFERENCE between the two signals though. Are you plugging in to the same input when using the adapter? If that's the case, then the preamp would not be the problem.

It would be helpful if you told us the name of the mixer, as that (to me) seems like the most crucial piece to this problem.