I've done testing at different levels and haven't noticed a difference yet, but I could try a level 1 Way of White vs a level 500+ Darkmoon and see if the Drift Item bags or resulting vagrants are any different.
I don't hold too much stock in the speculation about vagrants getting more powerful over time though, because much like other early Vagrant speculation, you have to wonder how did someone come up with that? It's not something vouched for the by the devs in the manual, guide book, or early interviews, so I think it was a baseless guess on trying to explain why some vagrants have better drops or appear as red.
The manual nor future press guidebook say anything about the items or vagrants 'improving', but an early article does have this to say (which supposedly has confirmation from the devs):
Things like discarded items and lost Humanity transform into different forms and wander through other people's game worlds. If people leave them alone without picking them up, they keep moving, eventually transforming into very valuable items.
You could see how someone might assume this means that the longer something sits around, the more it'll transform into something better. However, I think this bit of info more closely matches what I'm observing: An item is dropped, it turns into a cheap / useless item in drift item bag form, but then after not getting picked up and moving around to other worlds, it eventually turns into a Vagrant with a better item inside. How long it actually takes to turn into the vagrant, or how long the drift item bag takes to find another world, doesn't seem to affect what the item turns into.
Though another variable to consider is Vagrant HP. Perhaps they might have more HP based on some characteristic of the player who created them. Low level might mean lower HP, higher level might mean higher HP? The futurepress guidebook lists a range of HP values for both the Good and Evil Vagrant types. There's probably a reason the HP is listed as a range, because some variable probably allows it to change.
But stuff like what their HP is and whether or not different Evil Vagrants are capable of doing different amounts of damage though are on the bottom of my priority list for the time being.
Here's another Good White vagrant, with a slightly lesser soul item. I'd never seen this drop before, but I was able to predict it based on patterns I was seeing: