Without being specific, I've heard of an advertiser who added a word related to the concept of complete privacy to his ad title. The ads were for resort type rentals.
With the addition of that single word, his results got way better.
He'd obviously hit a 'hot button' with his potential customers.
So, it might be a pretty good idea to put yourself in your customer's life, sit back for a bit, and see if you can figure out what the hot buttons for your product or service are.
The ability to put a second or third ad in an Ad Group is ideal for testing this sort of thing. AdWords will rotate the ads evenly, and let you see the CTR for each variation.
IMO the title of your ad is, by far, the most important real estate in your ad.
This is because a lot of people on the internet just skim. They see the title first because it's bigger, blue, and underlined. In fact, it may be all they ever see, if it doesn't catch their eye
Also, if your title also happens to contain the keyword searched, it will be bolded too.
So, really make that title count!
Doubling of CTR by flipping the text in the two lines is possible, but very vey unlikely.
As AWA says, run two ads - the old one and the new one in the same adgroup (for a week). Let us know if you really see that kind of difference.