Your "sound" is affected by your posture through a) support and therefore airflow, and b) direct shaping of your mouth cavity and therefore resonance, and c) indirectly caused tension in other muscles/body parts involved in singing, such as tension in your jaw and/or tongue.
Singers, whether soloists or choristers, generally preferentially sing in standing position since that provides the least obstacles to singing well. Voice teachers almost invariably work with their students standing up, at least when learning the fundamentals of singing. However, opera singers will learn how to retain crucial elements of good vocal production in a variety of positions, including sitting, moving, even lying down.
It's also important to note that what one hears, while singing, of one's own voice, is tremendously affected by vibrations passing inside your body (e.g. jaw). In your situation, I would start by asking others and/or recording your voice and playing it back to first verify whether your sitting-down voice is indeed better than your standing-up one, since your perception of this may be an artefact.
If indeed your "sitting voice" is objectively better, I would suspect that there is something in your standing-up posture which is not right, i.e. where though standing up should be more conducive to singing well, you're doing something wrong which is getting in the way, a bad habit you don't fall into when sitting. Addressing this bad habit should then help you in any position.
As a singer myself, I've had to work on not standing too rigidly "upright" (I was actually bent backwards), on neither compressing my thorax nor having facial tension from lifting my jaw too low or too high. From tension in my tongue and jaw induced by keeping one hand rigid while standing. I've addressed these issues in part by various constructed exercises to move while singing, sing bent over and/or seated and/or leaning against a wall -- not good posture in and of themselves, but helpful to build awareness of and break bad habits.
So I'd go back to basics and follow (with a teacher or on your own) various guidance on how to sing upright with good posture and try to find what element you're missing. Part of this might involve standing up and sitting down and self-monitoring changes in individual elements of your posture and presence/absence of tension in different body parts while singing in both positions. What you're describing is unlikely to be a necessary or direct consequence of sitting vs standing, and much more likely to be an indirect consequence of how your body and brain have learned to interpret the instruction "sit well and sing" versus "stand well and sing".
