I have been through a scavenger hunt to find the results of all EP Balance Polls and compiled them in comparison with Tournament picks. You can find the spreadsheet
here. I will include a graph with both data and a short sentence to describe them.
Regarding Perceived Strength, it refers to data taken from all the pre- and post-tournament balance polls I could find in the forums. I believe one for EP5.0 was missing. The maximum value in the questionnaire was 10 and minimum 1.
Tournament picks have been normalised. Each value is divided by the maximum number of picks and then multiplied by 10. So, 10 denotes the most chosen civ and 0 a civ that was never chosen.
Aztecs were perceived somewhat strong in 2015, that perception has been falling until March 2020. A minimum was reached in July 2019. However, their tournament esteem is generally low.
One of the most popular civs. Its perceived strength is also quite high throughout the many iterations.
Chinese after a period of mistrust on their level during 2016, they gained momentum in the coming years. Not very popular in tournaments.
Initially their power was intermediate and a medium preference in tournaments. In November 2017, they appeared very strong, followed by a drop in the following year, resulting an increase in preference.
Another tournament favourite. Strength-wise they have always been considered significant, with little variation.
Great fluxuation in both aspects. Huge boost in 2016, followed by a steady drop during the next year. During the subsequent years, they hovered around the strong civs. Preference also has big variation, with a big spike during NWC LAN 2019. Yet, in general comparison are another players' favourite.
Their perceived power lies on the better side, with a small decline in November 2018. Interesting is the mistrust on the civ in the last Winter Tournament in 2020.
The black sheep of RE is assumed as intermediately strong, with a very low tournament preference, with a small increase lately. Since, their perceived strength shows an upward trend.
Primary perception of the civ was that is fairly on top. At the end of 2017, it shows a decline, however, recently an increase trend can be seen. They used to be chosen sometimes, but there is an increase in their actual popularity.
The other pariah of RE. Definitely considered as a very strong civ. A drop is observed in late 2017, and is steadily increasing since. Similar path follows the popularity in tournaments.
Portuguese were thought as somewhat strong, yet their popularity in tournaments is very low. During the years, their status has been stabilised. Interesting is the spike in Autumn 2018 and NWC LAN 2019.
Although Russians aren't perceived as top civ, they are highly popular in tournaments.
They were moderate to low on the strength comparison. A big boost is observed in November 2017, followed by a steady decrease. Their popularity is low with a rise during NWC LAN 2019.
Another civ on the medium-low tier. Their tournament reputation has also been low.
I found the balance polls by searching in the ep discussion forum. It was indeed very hard to find all those results. I used the search tool with term "balance poll" and went through 30-40 pages of results.
They used a ranking of 1 (weak) -10 (strong) and asked participants what they think considering the specific EP notes. For what I understand there wasn't any pr/elo restrictions. That's why I avoided focusing on the top players.
As for tournament preference, it's simply the total picks in the specific tournament normalised as explained in OP. Since tournaments are the main testing ground for EP and have a more serious setting than qs/ladder, the civ picks reflect in a fair degree what people think is strong.
Of course, you have the factor of people being familiar with certain civs and play mostly with them, but I can't think of a measure that accounts for that.
