Executing with Arms

Ok, so I've briefly put together some numbers on the cost/benefit to going for Execute vs. using Heroic Strike.

We'll assume in both cases that we've essentially talented and/or glyphed for each depending.

Ok, so in the Execute camp, here are the mechanics:

1st - Talents in Sudden Death, Improved Execute and Glyph of Execution

Mechanics:

-- Sudden death will proc infrequently, but at 9%, it will still happen many times during a long boss fight.  If we assume about 3200 AP, then the "maximum" damage you can do with an early execute will be about 3200 damage (give or take) at a cost of 20-30 total rage, making the damage per rage cost = 160 dpr.  If fired at 10 rage (the minimum you can use) the damage will be 2500 (give or take) at a cost of 0-10 rage.  That's correct, 0-10 rage.  The mechanics on Sudden death are configured so that each time you use execute, it "rewards" you 10 rage when it's done, so if you spend exactly 10 rage, you get that refunded to you, making the cost free.  

-- At endgame this comes into play as well.  The only cooldown you have to worry over here is the gcd, since Execute has no inherent cooldown.  Since you can use Execute at 10 rage, and since at 10 rage Execute is free, once the target hits 20% health, you can essentially SPAM execute for free, dealing approximately 2500 damage every 1.5 second global cooldown on top of your white strikes.  Of course, you'll probably do a lot more than this, because all those white strikes will be generating rage, but make no mistake, there's no point in pausing with this build, because the maximum damage you can do with Execute at full rage is about 5800 (give or take) and if it takes more than 3 seconds to completely fill your rage bar, you're better off going with 2-3 lower rage Executes than trying to get the single burst from full. 

Now in the Heroic Strike Camp:

1st -- Talents in Improved Heroic Strike and Glyph of Heroic Strike.

Mechanics:

-- During combat, you can use Heroic strike any time you wish, spamming it any time you have the rage to burn, there is no need to wait for a proc chance.  However, using Heroic strike has a 12 rage cost, and only does (again assuming about 3200 AP and a fairly good weapon) about 2030 damage on average.  Now, if we further assume a 40% crit rate, then we can assume that 40% of the time you'll be recovering 10 rage points from using it which "technically" lowers the cost to 8 rage, which makes this an impressive 253.75 damage per rage ability, but we have to include the 'hidden' costs as well.  Note that HS is not an instant attack, and note that you do not gain rage from an HS like you would from the white strike that would ordinarily be happening.  This also has to be factored in.  While rage generation is not typically a problem, rage generation while spamming HS is very difficult, as your white strikes are not bringing up your rage totals.

So in conclusion we can see that, ultimately, going with Execute over Heroic Strike as an Arms warrior makes good PvE sense.  During combat, you still have plenty of abilities to fire to keep yourself busy, and you can always blow a few HS's when you have the chance, but the ability to add an instant Execute during the lead in phase without disrupting rage generation from white strikes will keep your rage at good levels to pop for emergencies, while at the same time allowing unreal damage potential in the last 20% health on bosses.