The +10 armor = +1 all resist is true when your armor = 10 times your all resist. The relative gains however deviate from the 10:1 rule when you break that balance. That said, it isn't really possible to get the relative difference in numbers to the point where a 280 armor gem will beat a 78 all resist gem for pure toughness; your armor either has to be absurdly low, or your all resist needs to be absurdly high. In the last case where your all resist is really high, a vitality gem will be the ideal gem to use. Also, I think perfectionist and the boar stack additively to a total of 30% (not 32%) bonus all resist.
Consider the case where you have 4000 armor (below average), 1200 all resist (above average), and 4000 vitality (about average). This scenario favors armor more, but the 280 armor is still too low to be a big benefit. Then the relative bonuses for 280 Strength, 280 Vitality, and 78 All Resist are:
Base Toughness ~= (Vit*80)*(1 + AR/350)*(1+ Armor/3500) = 3.037M
Toughness w/ +280 armor = 3.150M
Toughness w/ +280 vitality = 3.249M
Toughness w/ +78 all res = 3.190M
Not even the fact that armor was better than the 10:1 ratio could outperform the all resist. Once you get your armor down to about 3000, and all resist up to about 1300 (without diamonds), then the 280 armor beats the 78 all resist; however, the 280 vitality trumps both options!TLDR; Don't bother with rubies in armor unless your class name rhymes with librarian or invader. If you want toughness, stick to diamonds and amethysts. See post below for choosing diamonds vs amethysts per socket.http://us.battle.net/d3/en/forum/topic/12673198817#8