Do you find that there are certain shots that will just always be snapshots no matter how much you want to capture them with great composition?
Yes - sometimes the subject matter better fits into the snapshot genre. The shot of your child sleeping is a good example. While we all want to be artistic, don't forget photography is about capturing the moment.
There are some people who seem to be able to take ordinary things and make them spectacular. I have a friend who can take a picture of some normal household scene and get 50 flickr comments. She just has something special.
Like many others have posted, some are born with the "gift", others have to work at it. That doesn't make those born with the talent any better than those not. Develop your own vision and style.
I wouldn't put much stock or faith in the comments received on Flickr. You don't know the background of those leaving the comments - they could be photography peers or just the average internet user. It's the internet, nothing more.
Remember, photography is capturing the moment along with displaying your vision and style. What works for your friend may not work for you and vice-versa.
Good luck.

Wow. No idea how you got desperate out of the OP. I said that 

