I just discovered DIN rails for industrial kinds of loads (10's of amps). I'm using these parts, and am wondering whether I should jump on both sides. It seems like more connections would mean lower resistance and that it could handle more current. This comes at the cost of consuming another jumper, though. Does it make a difference?
You could use a jumper on both sides of the terminal block, but it is unnecessary.
The reason that there are two spaces for jumpers on each terminal block is to allow you to jumper more terminal blocks together. For example, if you want to jumper three blocks together, but only have jumpers with two poles, you are able to do that by putting one of the jumpers in the upper jumper slot and a second jumper in the lower jumper slot, and the block in the middle would have a jumper in each slot.
The terminal block part you specified, Phoenix Contact 3044102, has a nominal current rating of 32 A (with a maximum load current spec of 41 A). However, the jumper you linked to above is not the jumper listed for this block. The correct jumpers are shown on the "Accessories" tab. The correct 2-pole jumper is Phoenix Contact 3030336, which has a maximum load current of 32 A, which means that you can use these jumpers in your application without having to double them up.
However, you mentioned ground junction points. If these terminal blocks will be connected to ground, it is best to use special ground terminal blocks. In the same Phoenix Contact series as the other parts, you might select Phoenix Contact 3044128. These ground blocks are electrically connected to the DIN rail itself (and the subpanel that the DIN rail is mounted to). No jumpers are needed, as the DIN rail connects all of these blocks automatically. That having been said, you don't normally push 30 amps through your ground wires.