Color is much more expensive, and from Jay's experience is much less consistent than black & white. Basically, if your market can bear a price where you can make a profit with the higher production costs, or if a profit is less of a concern and you're still able to price competitively, then it doesn't hurt to test things out and won't cost anything more than your time and a proof or two.
Your ability to price your book competitively will depend upon the minimum you can put your book onto the Amazon Marketplace for without receiving a royalty; namely, you can not price your book lower than 5/3 of the cost to produce the book because 40% of the retail price is reserved for Amazon's cut so you need to be able to cover the cost to print the book in at a minimum 60% of the retail price. Multiplying the cost to print by 5/3 is the same as multiplying the retail price by 60%.
The cheapest that you can print a color children's book (full color with bleed at 8.25″ x 8.25″) is $3.65 and that will cover between 24 and 40 pages. That means that you can't get it put onto Amazon for less than $6.08. If your market can bear a children's book priced at $6.08 or higher, then you could conceivably put your book onto Amazon. If you don't plan to sell through Amazon but only want to sell through other markets, then you only have to cover $3.65 plus whatever it costs to ship each book.
For comparisons sake, a similar book in black & white could be anywhere between 24 and 108 pages and would only cost $2.15 to produce and could be priced as low as $3.59 and still appear in Amazon's marketplace. That's less than the cost just to produce a color book at potentially 4½ times the page count.
As for Jay's books, he's only now putting his children's books into print, and has concentrated on Kindle up to this point. However, his books aren't full-color children's books, they're basically a regular book that deals with childish material and includes images that are basically black & white already (the small bit of color used in his images isn't really necessary – if you use the “look inside” feature for his Fart Book you'll see what I mean.)
Note that you still get a full color cover even if you have a black & white book, so for him it doesn't make sense to print in color anyway.