Had they lost a game, they wouldn't have made it into this thread. So it wasn't all for nothing.
My point is that the quality of a team isn't always defined by what they win. The reputation of the club is.
The Liverpool team under Rodgers that nearly won the league were better than the 05 team, that won CL, even though they won nothing.
I agree with that 100%. Most of the time, the best teams win the biggest trophies, but sometimes they don't. Leicester winning the PL, Cruyff's Holland not winning the WC are examples of such outliers. And I do agree that teams are judged on global perception more so than on quantifiable records, then logical arguments are made to embody that into a model of some sort.
I also agree with the your assessment of Rodgers' team vs the '05 team. But I really can't agree that the Invincibles tag, which you should carry with pride, is of more value to you than Big Ears. That's not true for all Arsenal fans, and maybe I'm just being thick, but I just don't get it - a record versus a major trophy. If it was the Mickey Mouse cup, the Charity Shield, or something of that irk, yeah, I'd go for the record. But if it was the League or EC title, there is no question which is of more value to me.
This is an opinion, of course, you can't argue with mine, and I can't argue with yours. I'm not trying to debate your priorities, it's fine to feel either way.