I get the corded drill thing. They are a hell of a lot lighter and fast. I need a drill that I can use while rapelling upside down 40 feet in the air over a theatre space, so I gotta have cordless. Although, the hybrid is an option, but not something I’ll pay for.
I have to agree with the 18v DeWalt, at least for heavy duty work. I just finished a cedar fence job, and the big DeWalt flat blew away the 14v Skil and the 14v “off” brand we had.
As far as just drilling goes, I don’t know, this is just about screwing. 
I assume you will use it for both.
Rough estimates:
The DeWalt could drive over 600 1 5/8" screws and several dozen 3 1/4" screws w/o needing a battery change. The other two could a little more than half that. (YMMV)
While the DeWalt got kind of heavy in the hand after a few hours, it was much easier to bear down on to prevent the bit spinning on the screw head. Also, the torque settings were easier to control re: screwhead depth (too much or too little).
I don’t know if it was just the extra 4v that made the difference, but DeWalt gets my vote.
Well, seems like 18v Dewalt is our winner. I guess it’s up to me to figure out if I need 18v or if I will soon enough to rationalize buying it now. I’m not a carpenter by trade, so I imagine 14.4 will hold me for quite sometime. It does occur to me that if I buy the 14.4, I’ll need 18, and if I buy the 18v, I’ll never need it.
But, hey, I’ll have a cooler toy!