You probably know this already but satellite photos need accurate elevation data to be corrected, so anywhere where the ground isn't flat the correction offset needs changing. Lantmäteriet has accurate high resolution laser data to be able to correct their photos, but Bing probably have a quite low resolution model. ESRI have lower resolution images, but seems to have higher resolution elevation data so I find their imagery to be better corrected than Bing. (It is possible to get Lantmäteriet ortophotos in JOSM but the legality about that is still a bit unclear so I don't do that myself.)

NVDB can indeed have positional errors or small local geometry distortions (quite common where one road connects to another). If you have a Strava account you can enable a Strava heatmap layer in JOSM it's great for checking alignment if unsure. If one only has NVDB and Bing to go on concerning positional information, I'd choose NVDB as reference. If one goes to the data source at Trafikverket I think there is information about positional accuracy embedded in the data, but we don't transfer that into our OSM model for the moment.

There's some more info about NVDB limitations here:
https://wiki.openstreetmap.org/wiki/Import/Catalogue/Sweden_highway_import/Import_guidelines#Typiska_fel_i_NVDB-datat

Regarding the question, it's much better to align to the correct coordinates. When I started out with OSM mapping the accuracy of the satellite photos was much worse than it is today. And it will likely improve in the future. The goal should be to map with as high quality as we can with the sources we have, and if you have a better third party source, use that. It's likely that within a couple of years we will actually have Lantmäteriets ortophotos (not only the historic ones) in the web editor and JOSM as an official imagery layer as it's becoming open data too, and then the positional accuracy will increase dramatically. If the buildings are already correctly placed from the beginning a lot of work is saved. Of course there will always be a risk that someone with lesser access to high quality data sources will come in and "correct" the positions, but in my experience it's quite rare. People mostly map new things, correcting old (like we do in the NVDB import project) is quite rare.