Most of the oil I am currently dealing with is about API 30-40. Pretty light.
Most of the tanks use DP for level. Some older and mostly smaller ones use floats in bridles.
DP is fairly accurate, and except for density changes, accurate. For most of our application, level is to ensure we don't overfill or suck out. For that, DP suffices. The density range is not enough to affect us. For custody transfer, we use positive displacement meters.
For hi/lo level switches, we use floats.
A float in a bridle works well, if it doesn't gunk up. Floats in a bridle is also cheap. Add a magnetic pick up and you get a remote signal too! On most grades, it works. We do have some heavier oils, and dirtier oils, and in those cases, things gunk. The other problem with bridles is they get dirty and freeze - so you need to wipe them once in a while and heat them.
Radar is relatively newer. In new tanks, they work and we are seeing mostly radar on new tanks. In old tanks, with internal floating roof, they are hard to retrofit, so, back to DP.
Hope this helps.