I love Civ V and VI about the same that I love GC3, although I don't play Civ V anymore because VI was a huge improvement for me. I also very much enjoy Beyond Earth, although it's based on Civ V, so I don't really play it much anymore either.
Between Firaxis and Stardock, I go in surges. I played Civ V and Beyond Earth almost exclusively as GC2 was winding down in its lifecycle, then took up Civ VI for over a year just to get the hang of it. "Over a year" must be explained, however. I play these very long games with slower timelines. Although I enjoy the saga-length games, there could be weeks or MONTHS between sessions and between the end of one game and the start of a new one for me. I'm an adult with a full time job and other responsibilities, so I need to find a balance in life; just like in the games I play.
No sweat, I still made sure I was a founder for GC3, and took that one up just before we entered the era of the Cruseade. For the last couple months, I've played GC3 exclusively, even though there was a major Civ VI update just as I transitioned. I'll go back to Civ probably as the summer ends in a couple months, or whenever I feel like it.
I tell you, life is GOOD having both of these games in such a good, playable, and well balanced state. I feel so fortunate to have such a well-made genre of turn-based games!
I love them all for different reasons, of course. I especially enjoy the exploration aspect of all of these games, but the strategy of setting up my fleets and making other preparations for combat and conquest also has a very strong pull for me.
I think the OP only got it partly right. GC3 can learn from the Civilization Franchise, yes of course that's true.
But both games do some things better than the other, so Firaxis can also learn from Stardock just as much as the other way around. I sure do hope that there are a few people on both sides playing the games from the other companies.
At the annualized prices of these games, almost nobody needs to think of them as an "either/or" proposition. We can mostly afford BOTH if we really want. So rather than a competition, I think of this as a big pool party. Come on in, the water is almost perfect!