Well-rounded often means the person seems generally capable of tackling a broad range of activities, though they may not be stellar at any one. A guy who does well in school, plays sports, can mingle well, has a good group of friends, etc. Balanced, normal, etc. Used in this sense, it's a pretty poor compliment and doesn't seem to be a description that one should strive to achieve. What exactly is this "well-rounded" person good at? Yes, you may want to be versatile and generally comfortable in a wide variety of situations, but you definitely want to kick ass at a narrower set of activities.

Building character is often used to justify grueling tedious work, regardless of its merits/value. Done right, building character would consist of valuable activities that improved upon an important skill or helped people. That is, one builds character by learning and by overcoming obstacles on the way.

These are basically two phrases that could be used to signify positive attributes/activities, but are usually used in stupid ways.