This is a very difficult question to answer. I am pretty much obsessed with two games - and have been obsessed for quite some time - Magic The Gathering and Starcraft. Each of them fall under both of your categories. If I had to choose though I would say Real Time is the best. It allows you to move at the same time as your opponent and test your ability to not only watch what they are doing but adapt to it so you can counter them and win the battle. Turn based, in my opinion is pretty much a slow version of Real Time. Still very fun, but not as quick paced.