I have both carter and takeda... but if I we're to give up one... i'd sell my takeda... but that's a big "if" i had to give up one... i won't if I didn't have to...
Carters and Takedas are both really nice. You'd be really happy with either one, I think - provided that you like the taller blade height on the Takedas (which I do).
As to whether you want to start off with either of these as your first... it depends on whether you are going to seriously kick yourself for scuffing up the blade a bit when you first start hand-sharpening, when you get a little chip in the edge, or maybe get a bit of rust on the blade, etc etc. If you're going to really fret about it and kick yourself for it, go with something that'll hurt less psychologically. If you can take it in stride and shrug it off as part of the learning process, I see nothing wrong with starting with something nicer - where you know you're going to end up anything.
Sometimes there's a benefit to starting with what you really want anyways: you'll end up spending less in the end that way.
I instinctually grab other knives daily; my Takeda only gets used when I cognitively grab it; if that makes sense. It's fun, sharp, everything a knife should be, but its quirky. For the price, I think a near perfect knife can be had.....
The difference between try and triumph is a little "umph"! NO EXCUSES!!!!!!!
Then there's thinness. I'm clearly not a pro, so take this for what it's worth, but given my admittedly poor technique the Carter is almost too thin--even w/ a light pinch grip, the rounded narrow spine still wear a sore into my index finger faster than any knife. Maybe the Carter you're looking at isn't so thin; mine is literally half as thick as a my Takeda. I love them both, you can't go wrong. I tend toward the Takeda, probably because it was my first really good knife and I used nothing else for six months, so I'm bonded to it like no other knife.