Hmm well its easy to see what archery +10% crit chance does, just toggle it on while holding the xbox (char screen DPS inculdes crit damage boost).
As for the other one well it hard to work out as like it says Crit chance resets 1 sec after you crit so the chance varies between 7% and 100% (31 secs after you last crit).
According to my numbers what will give you more crits?
Well the chance of getting crit is high in combat for archery then for Sharpshooter the time taken to hit 50% mark (that is 50% of people using your set up getting a crit by then) is using archery is between 3 & 4 seconds compared to sharpshooters where its between 4 & 5 seconds of combat.
And the chance of having at lest 1 crit is stays lower for sharpshooter until between the 7 & 9 second period.
^ Given this I say Archery is the best for that weapon, if attack speed was a lot slower then Sharpshooter would be a bit better.
Sharpshooter all of the way. The reason is many fold. First it takes 1 second to reset which means that everything in the initial second of damage crits. Watch all of the yellows in your opening elemental electric arrow. This makes your opening AOE attack way more powerful which is really handy.
Second you spend a lot of time Kiting. As you run away your crit goes up. When you are kiting you want maximum damage in the shots you get off behind you. Again the situation you want the higher crit. You will not shoot every three seconds while running away. So Sharpshooter helps when you get into trouble because the Barbarian died you can get out of it more easily.
BTW Brooding and fast run are also helpful for similar reasons. They kick in when you are in trouble. Brooding in particular means you enter combat at full health generally. It also means you heal as you run away.