Is there any difference in the way fish react to these? I wound up with each of these tied on yesterday and began to question the need for both of them as I was fishing them the same way.

T-rig typically catches more fish and comes thru certain types of cover better. A jig usually catches better quality fish (for me anyway).

-Jig gives more bulk when they want that. Works better for me on deep ledge presentations and produces better quality fish.
-T-Rig allows you to change baits when needed for color, size, tails and etc.. Just a better all round rig.

I've had good luck on the punch skirts behind a tungsten weight. You get the added bulk of the skirt and the more weedless qualities of a Texas rig. There are a ton of colors in the punch skirts. Some are bulkier than others. I've also done well with the Strike King Slither Rig but you are limited to just a few weights. Experiment with them to see what the fish want for that day.

Lol his impression of somebody fishing a jig slow is me.