I don't understand how the phillips is winning. I just recently decided to go with the corkscrew. My climber model should be getting here within a week. I went with the corkscrew because the climber was ten bucks cheaper than the super tinker. I'd get the one can find the cheapest, and if funds don't matter to you, get both.
It is important to note that you can use other tools on phillips screws, but you can't use other tools instead of a corkscrew, like opening wine (especially if you like it) and holding a mini-screwdriver bit. I also read that it's good for untying knots, but I'll have to see for myself. I think the corkscrew looks nicer,too, a little out of the ordinary in someone's pocket.
I got the climber as previously stated because I want this to be my "EDC" knife. I wanted to try out a scissors model. The next one on my list is the Alox Farmer (with a saw), which I'm planning on getting for woods work. I think the scissors vs saw depends on your intended use. I really don't see myself ever needing a saw unless I'm in the woods, where there is wood needing to be sawed... You should think about whether you are getting this for camping/hiking (saw) or EDC/indoors (scissors).