I have both, each for different applications. The auto tuners are great for ease of use. You push the button, it loads up the antenna for you. There are some auto tuners that are made to attach right to your rig of choice, making a nice compact package. I use the LDG auto tuner that attaches to the Yaesu FT897D and it makes a great portable rig.
With manual tuners you learn to adjust it yourself. Once you know how to do it, it doesn't take long. Because they are manual, there are WAAAY less parts. You can build one yourself for not much money! They also can load up pretty much anything, where an auto tuner cannot. Manual tuners are more easily built to handle a lot more power, which is something worth considering. I use a manual tuner on the base, especially when I want to run power or want to load up my wire antenna on a frequency that is way out of its resonant point.
They both have a purpose and you may end up with both over time. What type of antenna are you going to want to load up?