Do you start fine tuning the system with cables or tubes ?

Tube differences can be easy to discern. It depends a bit on whether you start off with basic OEM tubes, or whether you roll between various third party tubes. Upgrade from basic has been instantly recognizable, in my experience. Third parties may or may not be discernible. Some are also more a question of flavor, and preference may depend on what recording you play. As I listen to a wide variety of music, if any piece of equipment does not make all music sound better, then the it does not matter. I do not keep separate sets of tubes for baroque strings vs. EBM and switch them accordingly. And there is the habituation factor as well.

I have yet to hear any difference in any cable. Yes, I tried, and no, I have not heard any difference ever.

Tubes in most cases. 

Tubes definitely make a more discernible difference in my experience.  The biggest impact I have had with tubes are 6SN7 and rectifier tubes. I could not believe the difference a Mullard GZ34 made to my system after inserting it into my Allnic phono power supply.  It was akin to a component upgrade.  

I have also owned and tried a ton of cables. not as impactful as rolling tubes, but more of the final seasoning to the soup. The system and the room need to be addressed before dropping large sums of investment in cables IMHO.

Yes, assumption is that both the cables and tubes are already quite good. That's why I called it fine tuning, your system is tuned but you want to take it a little higher without changing active components.

In my case, cables are excellent and I don't think about upgrading them because it would make more sense to upgrade analogue front end and speakers before doing it. So I proceed with tubes, though here too I believe I have found the right balance for my VAC Avatar SE integrated. One could do better but at high cost.

Neither. Your system should sound good with stock tubes and basic, well  designed cables. If something doesn't sound right, fix the problem. Using tubes and cables to fix a problem is almost always a bad idea. Once you get everything sounding OK, different tubes an cables can be used to enhance an already good sounding system.