You can check the side by side comparison of the 2 phones, click here.
As I checked the comparison, although the LG Optimus Showtime is the newer phone, I can definitely say that the Samsung Galaxy S II is still the better phone.
The Samsung Galaxy SII by far but then you have to look at the price you are paying for each as well. You cannot expect to get the same features etc., out of the LG Optimus Showtime when it is hundreds (in most cases) less. However, for the price, the LG Optimus Showtime holds it's own and in it's class with say the folks who purchase it from Straight Talk, it's totally hard to not find rave reviews. So if you cannot get the Samsung Galaxy SII because of financial limitations at the moment, go for the LG Optimus Showtime. I really think you will be happy you chose the Showtime, at least for now.