One advantage of Lat/Long is that you can get it by sighting on the sun moon or stars as long as you have a watch with you.
If you are good at it you can get your location within about a mile. (1.6 kilometers)with pretty simple tools. Traditional navigators like it more.

That is not accurate enough for fine map work so when you are located on your map and doing survey work you usually use surface measurements. So miles or meters instead of degrees and seconds.
Surveyors like field measurements off grids more than angle measurements from stars.

With the UTM grid system and GPS units available you can locate on a mapped grid to within a few meters easily.
Modern GPS units can locate a surveyor to within 2.5 cm.
As Sarbound points out, with UTM you have an easy distance measurement that you don't really need to think about while with Longitude you have a reading you need to convert to ground measurements.
Universal Transverse Mercator does have a couple of other problems which Yelp's answer points out.
There are many different grids in use and they all vary on where their data points are. The data points (datum) is their model of the shape of the earth. It also involves the grid system they laid over it to measure from.
If you are using the wrong grid system it can throw you off.
The short of this is that you need your maps and GPS unit to be on the same datum. The datum will be noted on your maps.
They also need to be the same for the people you are communicating your locations with.
In North America the standard datum in use is North American Datum 83 which is also used for north America in the World Grid System 84.
However if you have an older map it might be NAD 27. Some USGS maps have grid marks for both. Military grids can be different too.
Usually the difference is only a few hundred meters between NAD 27 and NAD 83.

I think this was a good thread to start.

I use UTM for almost everything. It is easy to measure on a map with a scale card. Most of the time you don't even need the card and just estimating the grid is close enough.