Kat and Shyv are fundamentally very different champs. Their only similarity is both being melee.
Kat is usually taken mid lane as an AP assassin. Since you're melee and squishy, you're fundamentally weaker in lane than an other ranged champs mid. As a lot of other people have mentioned, Kat is very much about taking advantages of other player's mistakes and snowballing from there. You're main job in fights is to play cleanup crew, since your passive gives you resets the more people who are low and will give you resets, the better.
Shyv, on the other hand, relies heavily on auto attacking to kill people. You have mostly single target damage (asides from w) unless you're in dragon form. Shy usually goes in the jungle and requires quite a bit of knowledge about jungling to play well. (She's not the best ganker, but quite a good counterganker.) She's played as tanky dueler. It's honestly entirely up to you who you pick depending on what you like to play. I would personally recommend Shyv between the two, but there are definitely other melee champs that are easier that you could learn.
If you really want to get to know melee champs, I would suggest looking into playing toplane, as that is the lane where most melee champs go. (Some current popular ones that I can think of atm are Jax, Mundo, Gnar, Trundle, etc.)