Count me among those thinking, "How can we answer your question--doesn't number crunching the benefits count as min-maxing?" That said, I am generally of the opinion that a Dex Fighter is the better "overall" package too.
Strength gets you higher damage...if you're willing to forgo the highest AC (can't use a shield with those 2h weapons!). Strength potentially gets you the highest AC...but you'll have the same damage output. Strength gives you "athletic" skills, which the barred door gives as a decent example--but you'll be




at all the Dexterity skills, which may be more useful (and almost certainly better at risk avoidance) in the long run. Strength saves are rare, but might be slightly nastier; Dex saves are quite common, especially at lower levels where (IMO) failing a save is the most seriously dangerous.
I really think "excellent Initiative and stealth skills" is a better deal than "highest AC ~or~ highest damage, plus athletics." In most other ways, the two are comparable, or (IMO) Dex slightly wins out. There are no mechanical disincentives to Dex (not that I think there should be), and winning initiative is always a huge boon no matter what you play.
I can agree with the "you should probably have at least one person with good Strength in the party" line--but I worry that that's a
bit (JUST a bit, not a huge amount!) like the old "somebody should play a Cleric" line. That is, with such seemingly-great benefits from Dex, what do you do if nobody *wants* to play a Str-based person? Obviously if you DO have someone who wants to, you're home free.