Higher risks of baby getting GI illnesses, higher risks of baby getting allergies, and a higher risk of the baby developing a variety of illnesses later in life. These risks have been documented in a large variety of studies, although usually phrased as "advantages of breastfeeding" (ie: breastfed babies are healthier") rather than as risks of formula feeding (ie: "formula fed babies are sicker.")
If you have a medical reason that you can't breastfeed, or that you can't produce enough milk and need to supplement, then the best choice is donated human milk. The next best choice is some kind of formula. I would guess that organic formula is "just as good" as conventional formulas in terms of infant nutrition, but with fewer pesticide residues. However, not all babies can tolerate "regular" formula, and the specialized formulas aren't available in organic.