I may be partial to my own crochet, but I think my revised version (right side, worked in the round, no seam) looks nicer: the stitch definition is the same on every row. The yarn used in the revised version is a continuation of the same skein of Patons Lace (Fiber Content: 80% Acrylic, 10% Mohair, 10% Wool; Yarn Color: 33129 Porcelain; Yarn Weight: 2, Sport/Baby).
As an observer noted on my Facebook page, I don’t usually use/recommend natural fibers for infant items, because of unknown fiber allergies; these are just samples.
I rephotographed the first one because I had folded the brim wrong. As you can see they are the same size for the most part despite the left one having a 25-stitch circumference and the right one having a 24 stitch circumference.