I'll have to check on the damage when I get home. I wonder if there's a threat generation difference.
On my Shadow right now (I don't have Applied Force; if you have it, it looks even worse for Shadow Strike), Double Strike hits twice for 681-781 damage (1462 average pre-mitigation); Shadow Strike hits for 2177-2496 (2336.5 average pre-mitigation). In addition, DS has a 51% chance to make your next Project a guaranteed crit (which amounts to 34% more damage with Project, for ~290 additional damage) so it's really ~1750 damage compared to ~2340 damage. They both take a single GCD so, without Infiltration Tactics, Shadow Strike does ~33% more damage at the cost of ~4.6 times as much Force ((50-15.6)/(23-15.6); this is ignoring any situation where you might be dodge/parry/blocking and getting more Force back, wherein the ratio looks even worse for Shadow Strike; with 2 Force/sec more, Shadow Strike costs 6 times more). You're getting *marginally* more damage frontloaded, but you're costing yourself *way* more damage over any time frame afterwards because of the prohibitively high cost of Shadow Strike.
Honestly, I wouldn't use either Shadow Strike or Double Strike as my opener. The best way to generate threat, damage, and mitigation as a Shadow is to follow the Thrash/DS-less rotation: you would remove Shadow Strike from your bar completely, open with either Project or Slow Time (and keep them on CD), while only touching Double Strike 1-2 times a minute when everything else is on CD and you're above ~70 Force.