First I'm going to mention why high Quality Score (while in my opinion the better of these two metrics to chase) is not what you should be after. The above linked to post does a good job of arguing against why the data is flawed so there is no need to go there. I honestly feel that no matter how well QS may actually effect yours ads placement or bid price it's not the metric you should be after. Quality Score is a made up metric used by Google to serve ads. Google is nice enough to give us the scores but I honestly don't feel that Quality Score MEANS anything to us as advertisers. I'm not saying you don't want to have a good Quality Score and you should not optimize your ads for better QS. I'm saying that having a high QS by it's self means nothing!
Now on to Click Through Rates. Why I think having a high CTR is a horrible goal to have by it's self. First lets analyze what High CTR really means and then why I think its a horrible metric to chase.
For the most part anyone running a paid search campaign is on a PPC model. This means that you pay each and every time your ad is clicked. Naturally you want your ads to maintain a certain CTR letting you know your ads are working or at least being clicked on at a reasonable rate. The higher your CTR the cheaper your clicks will usually be which is why most marketers chase high CTR. However Google gives you cheaper clicks when your ad is clicked more (high CTR) because THEY MAKE MORE MONEY, NOT BECAUSE YOU DO!
Higher CTR = More Money Spent
Now you can see why I don't feel optimizing ads on CTR, the rate at which Google makes it's money or Quality Score, the score Google gives you for how well you make Google money is a good idea. There is 1 and only 1 metric I feel you should be optimizing your paid search ads on.
That metric is CONVERSION RATE. The rate at which you or your client makes money.
At the end of the day unless the changes you make to your ads equal more revenue the correlating data (CTR or QS) means nothing but wasted ad spend. The lessons you learn themselves have value but this helps clients bottom line little.
I'm going to state one more time that I DO feel increasing QS and CTR will help your ads performance. I just do not feel they are good metrics to chase in and of themselves. Focus on revenue growth and you will never go wrong.