You know what, I don't actually have a single well proven solution :- ). I experimented with a lot of concepts, the following is by no means deep analysis, but just inspiration to try stuff:
1) Very soft (0.01-0.1) and large (but not crazy large, so 4-6 size let's say) Sun pointed into scene, natural temperature, or slightly less saturated temperature (-1000 Kelvin). Sky natural, or slightly less saturated (-25perc. ?).
Simulated diffused Sun behind Clouds pretty ok-ish. Maybe my most used scenario ?
2) Fully physical daylight setup, but the Sun is pointing away from scene, maybe bouncing from opposite facade. This is very interesting scenario because it describes lot of situations in which those scandinavian old apartments are being shot.
The streets are narrow so Sun hits something only partially. But this is technically hard to execute, it requires higher GI intensity cutoff (in Corona, the MSI parameter) and ideally...reflective caustics from opposite glass windows. Well...pure craziness. So it works just partially, but the diffuse Skylight and diffused Sunlight (by spreading and bouncing from opposite facade) creates interesting light.
This is hard to pull off scenario, I never did it successfully much to my liking. It will also render endlessly regardless of GI, Caustics, or Portal lights. In every renderer.
3) Romullus told me this once: You can set the Sun to 0 and it doesnt' actually deactivate it, as even 0 intensity Sun still modulates the Sky's Intensity and Temperature. It's interesting hack. You can put it further into Desaturation node.
This should work in multiple renderers because they all use the same Sun/Sky models these days (Hosek&Wilkie).
4) I play around with gamma and haziness parameters to simulate different low-horizon overcast skies. This can get pretty unrealistic by itself in exterior, but in interior you can never tell what happens outside exactly so that's ok.
5) Some of my overcast scenarios are just pure white color if the architecture did all the work. Like 255/255/255 in Environment Slot and plane to avoid floor lighting :- ). I did this for the patio rooms in Impremta project. Complex architecture defines light perfectly by itself so simplying the source of light can really put focus into architecture as the main light actor. This of course, absolutely doesn't work for penthouse with big glass windows staring into void.
6) I never did the ultra-big sun light (<10) but I've recently seen other studios pull off this trick. You basically act like it's not even sun...but some artifial spotlight reflector, like studio photoshoots for Poliform or BB Italia photoshoots, that kind of style.
- I don't really rely on the the Sun/Sky itself, but it's by basic setup to go to because of flexibility. I can really milk the system to create almost any kind of reality occuring HDRi in terms of interior light. Exteriors are different case altogether, it would not work there. But I really try to play with light modulation with using bounce cards, blockers, soft boxes, barn doors, recently even reflectors & spotlights to get more dramatic effect.
My setups are once again getting lot more complicated and I feel like there is far too much I don't know and I would really love to have opportunity to shadow some high-end studio photographer (ideally furniture guys).
We shot some HDRi for our own use, and they are brutally calibrated, nothing like on market. But.. I was never quite happy and successful with the approach of "drop realistic light into scene and watch wonders happen". It works for exterior scenes that are partial towards such approach (curvy surfaces, reflective materials, lot of glass), it works amazingly for studio setups and automotive renderings, but I've found the results in interiors are identical to what I can get with Sun/Sky, but I lack the freedom to changes stuff as easily.
Other artists seems to get fantastic results though...so this might be just my deficiency. But someone here recently summed my feelings and experiences super well with story like "I spend whole night trying 100 Hdris and then go back to Sun/Sky". And that was me so very often...