Let's see some examples.
"I shall go with you."
"I would go with you if I could, but I can't because I already have another appointment."
"If I were you, I would go hiking tomorrow as your leg is injured, but this is just my advice because in fact I am not you and shall never be you. I myself shall definitely be going as I love hiking."
So you see, if you say "I would", it doesn't mean you will do it or even intend to do it yourself.
If you say "I shall" it means you will do it or at least intend to.
That's a big difference, isn't it?