there are different classes and schedules for a given size pvc pipe. the outside diameter is the same while the inside diameter will vary

The advantage of the thicker wall is just what you've discovered.. it's stronger and stands up to a shovel better.

The disadvantages are that it costs more (marginally, but if you did a large system or a lot of systems, it would add up) and that thicker walled pipe carries less water. Depending upon the design of your system, the water may be forced to move at a higher than recommended velocity, as if you used a smaller diameter pipe.

Most often, class 200 pipe is used for lateral lines (between the valve and heads, only under pressure while watering). It's a thinner walled pipe, but not the thinnest out there. Sch 40 is usually used for the mainline pipe (always under pressure). It's probably what you've seen as the "thick" pipe. The fittings are the same since the outside diameter is the same.

I like to use latex gloves (like hospital exam gloves usually available in the paint department) to keep too much primer from getting on my hands.