Teshuva mi'yirah is basically when one realizes that the sin that he did is not without consequence and he therefore regrets having done it and wants to erase it. In a sense though, he is still living in the self centered fantasy world where his focus is still on himself and he's worried about his future.
Teshuva mi'ahava is when a person wants to drop the whole fantasy world and return all the way to Hashem. He realizes that the fantasy world of "self" has nothing for him and Hashem has everything for him. His aim is not to erase the sins per-se, rather it's to turn his life around and really return to Hashem. He has come to understand what Hashem told us: "Choose Life!" Hashem is the source of all life, all existence, all happiness and all good. And pushing Hashem out of our life is the source of all trouble and all problems.
In theory, both paths are acceptable. But the good news is that Hashem loves us to much to let us continue wasting our life in the fantasy world. He wants the best for us, and since He's the Boss, we don't have a say in the matter. And so He put us in a situation where the Teshuva Miyirah approach simply can't work for us addicts here on GYE. Here are some reasons it can't work:
1) The Zohar says (Shemos 214-b) that the only Teshuva that works for p'gam habris is "Teshuvah that is worthy of covering over all his deeds". R' Tzadok (Tzidkas Hatzadik #243) explains that this means Teshuva mi'ahava, which is a complete return to Hashem. Teshuva mi'yirah erases the sins - and these sins are not erasable. But Teshuva mi'ahava doesn't erase the sins, rather it is misaken them (fixes them) and turns them in to merits.
2) An addict (even a relatively mild case) is much too entrenched in his behavior to stop the behavior without a major change in his whole life.
3) In our generation, yir'ah doesn't talk to most people very much. Even if it does talk to you, chances are that it can't affect your behavior that much. In fact, it can very often have the opposite effect, making us all the more desperate for distraction.
Teshuva mi'ahava, on the other hand, works for all people, in all situations. As soon as you start to taste what it means to live your life with Hashem, you would never dream of going back to being the person that you were before; a person who lived a life of never-ending pain.
In the tochacha of parshas Bechukosai - which Chazal say is referring to churban bayis rishon, we don't find anything about Teshuva mi'ahava. Rather the pesukim talk about how the sins will get erased through the suffering. But by the Tochacha in parshas Ki Sovoh - which is referring to this golus, we find nothing about atoning for sins, rather it talks about how after we suffer the curses of being far from Hashem, we will return to Hashem with all our hearts, and Hashem will have mercy on us and gather us in from around the world, and He will circumcise our hearts to love Him with all our heart and soul - so that we may LIVE.
This is not about making peace with Hashem, rather it's about "I shall go and return to my first love". We finally realize that there is no other way and we turn our whole life around.
The Zohar says: "If people would know the love that Hashem has for the yidden, they would roar like lions to run after Him".
Hashem is - Kaviyochol - crazy over us, and He is waiting for us with open arms. We have nothing to fear, as Yehoshua said: "Hashem is with us, do not fear them" shortly after the chet ha'egel - the mother of all sins.
Hashem just wants our hearts, as it says: "Give your heart to me, my son". And when we give it to Him, life becomes SO SO much better!
On Rosh Hashanah, we are going to stand in front of Hashem in judgment. Instead of trying to bargain with Him, let's tell Him: "Yes Hashem, all I want is You, there is nothing else. Please help me get close to You, and please give me a year of Kirvas Elokim".
That is Teshuva Me'Ahava.