There are a bunch of different Shadow types in Persona 3 so I decided to make a page to give you a quick little break down of each one. First off I would like to give you this important piece of information. When you see a shadow, the size of it dictates how many enemies you'll be fighting not their strength.
First up, let's take a look at what a really difficult shadow looks like. I figure it may be smart to teach you what the baddest of baddies look like first! They have a reddish glow to them and despite the fact that they are marked as "really hard" in the game, I don't consider them to be. They have weaknesses just like regular foes. They do have a lot more Hp and hit harder - thought it shouldn't be anything you can't handle.
The next type of shadow (in the picture below) is a distressed shadow. This one is so much lower level than you that he's scared to even fight you. He's going to give you really crappy XP and it's best you avoid these guys all together.
Finally we got a rare shadow. These guys drop coins on the first floor that you can vendor for quite a bit of yen. On the later floors though they drop Nihil weapon customizations which you can use at the shop in the mall later in the game. June I believe the store opens, Mitsuru and other characters will remind you in the game a few times.
That's really all there is to know about shadows in Persona 3! If you have anything else you'd like to add or share let me know in the comments below!