If you're going to keep your phone for more than 20 months, then just pay the $199 up front if you can. Even if you keep your phone for three years, you're still ahead at $9.99/month for 36 months or $199 for two years plus $10.96/month for another 12 months. Even after 4 years, you still wouldn't have broken even between the two.
However, if you will keep your phone for 20 months or less, then do it monthly. Or if you do not have the money up front.
I do HIGHLY recommend AppleCare as screen replacements performed by an Apple provider will only cost you $29. All other damage (including accidental water damage) is $99. Last time I had a screen repair done third party (on my 4s), it was something like $80. My phone also did not function properly after the second one.