I'm not particularly convinced that it is harder emotionally working with sick children, whether as a pediatric subspecialist (e.g. neonatologist, pedi heme/onc) or as a surgical subspecialist (e.g. CT, NS) than it is with adults. Certainly some folks find it so and don't want to do this.
However, most folks who make the care of children their career not only like being around kids, but generally find them resilient patients who are enjoyable to care for, even when they are seriously ill. As far as having patients die, this is no fun in any field of medicine. In pediatrics, as hard as it may sound, doing ones job well - that is, ensuring that the child doesn't suffer needlessly, that the family is well cared-for, and that you've done the best you can for the child, has it's rewards too.
The toughest part of being a neonatologist from the emotional end is having to give families really bad news and help them understand its consequences. Nonetheless, one gets used to it and it's part of the job. Learning how to deliver such news effectively and compassionately takes time and can only be learned from observation and experience, mostly experience.
The positives of taking care of very sick children are substantial too. Many do very well, in all fields. Even those with substantial long-term health problems can have lives that are positive for them and their family and are not a burden to provide care for.
Bottom line is that to do pediatric care, especially for children with very serious conditions or who are critically ill, requires accepting what you can and can't do and enjoying and appreciating the opportunity to work with kids. That isn't so bad emotionally, I think.