Right, numbers.
Using the formula wowhead gives for shield slam AP scaling, we get the following:
((Attack power * ($gte(level, 85) * 0.75 + $gte(level, 80) * 0.4 + 0.35) + 7898))
$gte refers to which expansion it is, and since our level is 70, both return 0 as an output. This changes the formula to this:
((Attack power * 0.35) + 7898)
What this means is that, for every 100 AP, you get 35 more damage on shield slam for a level 70 prot warrior. This means that for every strength gem, we get (after buffs) 20*1.05*2*1.1 = 46.2 * 0.35 = 16 damage added to shield slam.
But, if at 74 (highest scale level for bgs), we get 0.787113% more damage per 20 PvP power. This means that for a basic gearset (1k AP) shield slam damage is (1000*0.35 + 7898) = 8248 damage, and PvP power adds .787% more damage (8248*1.00787-8248) = 64.921 damage, so 65 damage.
So to reiterate, at 74 (highest scaled level in random battlegrounds), strength adds 16 damage per gem, and PvP power adds 65 damage per gem.
Tell me again, how was strength better than PvP power?