as for the difference between felony and misdemeanor, that also depends on the jurisdiction. obviously, a felony is a more serious crime. it normally involves jail time. in federal court, it also can determine your rights to counsel (if jail time is greater than 6 months), as well as your ability to use a conviction in evidence (felony conviction always, misdemeanors only if it is a crime involving veracity or honesty).
felony neglect is just the level of seriousness of the underlying charge (child neglect) - which means it's pretty serious. but third degree is a lesser charge than say, first degree, so its not totally damning. i am interested to see if the defense calls for a probable cause or preliminary evidence hearing - which would force the prosecution to show them what they have.