Some people love hand corkers, some hate 'em. I'm in the second group. However, I would GUESS that most synthetic corks will be easier in a hand corker than some cork corks.
Hand corkers seem to work best with #8 corks (22mm across). The synthetic corks that I have used (I think I've tried 4 different brands) all seemed like #8 corks, although I haven't done an accurate measuring.
I personally use a portugese floor corker and it is very easy. I have friend that uses the 2 handed corker you are refering to and he says it's very hard to use and breaks corks. The floor corker is the way to go in opinion
I agree that floor corkers are the way to go. They are easy to use and I have never had a problem with synthetic corks other than a few times where I didn't use enough pressure and had to remove the cork. All in all though with a floor corker I can cork 25 bottles in about 10 minutes.