I have shirts from both and I can tell you that in my experience CEGO is vastly superior (not even close). Carl is a master at fitting you so you will get a much better fit (though, I measured myself for my Chan shirts so I don't know how it would be if Chan actually measured me). Carl has a much greater selection of fabrics than Chan (I stopped using Chan a while ago for shirts because of lack of fabric selection). The fabrics of my Chan shirts are pretty crappy, even for the price of the shirt. Also, for me, Carl created a specific collar that he thought would go well with my face and build and the collars on my CEGO shirts are by far superior to the collars on any other shirt I own. I don't know what it is about the collars but they look and feel better than the collars on my shirts from Chan, Hemrajani, and even many high-quality RTW shirts.
The only things that Chan has on Carl is that they will put think MOP buttons on your shirt at no additional charge (I believe you can get MOP buttons from Carl, but he charges extra, though, the plastic buttons he uses are nice as far as plastic buttons go) and they do a better job at pattern matching. At the lower price points on Carl's shirts (which is what mine are, IIRC my CEGO shirts range in price from $100 - $150), which are MTM, there is no pattern matching (unless it just happens to work out that way accidentally), while Chan does a pretty good job at pattern matching.
I don't know, I would go to Carl over Chan just for the fabric selection, never mind the expertise you get from working with Carl.