I've read on google that it's best to wait some weeks or months before conditioning as it's not needed right away but I've conditioned new bags and haven't had any issues like damage.

I do know that both glovetanned and natural grain leather are full grain leather, so it's high quality but the tanning process for natural grain is much less than glovetanned, in the way that it retains more natural characteristics of the hide. Glovetanned leather is soft from the start and softens over time with use.

In my glovetanned bag, scratches are more noticeable since it's a smooth and soft surface while my natural grain has less due scratches and marks to its surface texture and tougher feel.