The inner covers I use are reversible, a shallow side on one side and a 2" deep side on the other. the shallow side is for summer, and prevents the bees from gluing the lid down as Perry mentioned. I also have a hole in the center of my inner covers that I can put a jar of syrup in, OR, put a gallon bucket over. Then it is easy to feed when they need it without actually opening the hive.
The deep side is for winter, and allows space for winter pattys/sugar cakes etc... winter emergency feed if they need it. I can also store my 2" foam in the deep side for summer, and prevent some heat from entering the hive, fliup it over for winter and put the foam on the shallow side with the tele cover on top to keep the lid from condensing moisture.
I have mats, I tried using a mat on a single hive... First, I did NOT like the fact that it sagged down on top of the top bars, preventing the bees from crossing over the top, if they needed to get to the other side they had to go back under..
Second, the bees glued it to the top bars wherever it touched them and required peeling off. After that I never put it back on the hive again.
I am not saying DONT use them, because we all have our own preferences... I was drawn to them because they were cheap. If they work for you, then go for it!