I think at 0:15 of the first video you absolutely do have an example of a throw that you don't see Barkley make enough. That ball is 46 yards through the air on a rope on the deep post and it would have been good in tight man coverage. It's a great throw, and a great example of why I say that Andrew Luck's arm is indeed stronger than Matt Barkley's.
Similarly, at 0:15 of the second video, he rolls out to his right and belts out a 54 yard (through the air) ball on a rope off the roll to his right side. Superb throw, shows a good arm.
And then at 1:06 of that second video, another throw. He's falling to his knees but still belts the ball out about 48 yards to it's target. It wasn't a pretty ball, but he was falling to his knees while he threw it. This shows arm strength.
However, what's interesting about all this is, you have two videos that are highlight videos, and they span a bunch of games, weeding out plays from 2010 that were super impresssive, while ignoring the rest of the plays...and yet in all those videos...we've got three examples of throws that I can look at and say that's a really great throw on a ball I don't see Barkley throwing very often, if at all.
That's why I take issue with the term "significantly" better arm strength. It's not semantics. On 95% of the throws that you see Andrew Luck making, he's not throwing a more difficult pass, or getting more heat on the ball, than what Matt Barkley does regularly. It's just not happening. If you disagree you disagree, but I think most people if they see the throws side by side are going to agree with me. If you're only seeing the difference in arm strength on those rare occasions, then I don't think that's a "significantly" better arm.
I think that Brandon Weeden has a "significantly" better arm, and you can see that in any tape you watch him, because you can't get 5 minutes into any tape of him, whether it be an individual game tape or a highlight mix, without picking up 5+ throws you can put up side by side with Luck or Barkley and say these throws showed a better arm.