For reference, each has a 60% chance to remove a condition on crit with an ICD of 10s, the difference being that Generosity actually transfers the condition to an enemy instead of strictly removing it from combat.
So while Generosity is the better choice for a single-wield weapon set, I would like to use them together on dual-wield sets.
Internal cooldown sigils do not work with each other. Only one will take effect and both are set on the cooldown. Now as for which sigil activates, it seems to be a specific order but no one made a list. Most people say it's safe to say the first weapon's sigil takes effect. Same for stacking sigils (one works).
all sigil share cooldowns, once a cooldown has started no sigil with a cooldown will activate until the original cooldown has finished. For on crit procs whichever procs first triggers the sigil cooldown. However if you have two equipped at once you can get them both to proc at the same time (but they both have to do it off the same attack\tic)
For sigils that generate stacks the mainhand takes precedence over the left. If they are the same stack and intensity (both superior bloodlust for ex) you will get double stacks though.
Absinthe makes the heart grow fonder. http://i119.photobucket.com/albums/o160/The_Original_Latronis/33865d18.jpg