I've been finding that I have to tweak the temperature of the PLA much more than ABS, with two 'variables' - the specific filament, and the speed of printing.
In terms of the material, I have some PLA that prints great at 40 mm/s at 170, some has to be higher (180 or 190) to bond well at the same speeds. The variable isn't just the source - different colors have different additives that have different properties related to printing, even for filament from the same supplier.
In terms of speed, I have to raise the temperature when going at faster speeds. For example, if I printed at 40 mm/s at 170, I need to be around 190-200 at 120 mm/s. I'd guess that had to do with the filament spending less time in the extruder hot end, so if the extruder is 190 my guess is that the filament ends up coming out around 170.
I have to give 'props' to Jetty Sailfish, which allows you to override the temperature in the printer rather than re-slicing - that makes it much easier to tweak temperatures to do this sort of testing.
In terms of filament diameter, ever since I switched to Emmet's "minimal Mk 8" extruder, that's been a non-issue. I assume that with extreme variation would cause the extruded volume to vary, but so far I've used several suppliers and not seen this affect my prints.