Both measurements are useful, but ultimately they become most useful when you have some first hand experience on a given waterway. You need to know what constitutes a low flow, high flow, flooding, optimal fishing flow, etc. before the numbers tell you anything.
Once you are familiar with a waterway, seeing the flow or height will tell you almost exactly what to expect. Further familiarity with the stream and the USGS data will allow you to predict conditions pretty accurately at a glance.
Also, often a particular stream does not have a gauge but nearby creeks or rivers do. Learning how a creek compares to others in it's area is almost as good as having a stream gauge for that particular water.
For what it's worth, I also rely more on the cubic feet per second data than the gauge height. I just find it easier to visualize and also easier to compare different waterways using the cfs info.
The graphs are also extremely useful. The current flow and height may be ideal for Stream X, but if the graph shows a line rapidly sweeping upwards I know that the stream will soon be too high to fish, for example. or at least I know it may becoming muddy. On the other hand you can tell if a stream should be clearing up after high water. but again, you need to be familiar with the creek to some degree before you can predict these things. One creek may be clear a day after the flows level off, and another creek may be clear three days after flows level off.