In Likutei Moharan Torah 110, Rebbe Nachman teaches an interesting concept in regards to sighing. He compares the sighing of a Tzaddik and that of a Rosho, and which sighing is better. If a Tzaddik sighs, chas v’sholom, in yearning for wickedness, this is a horrible thing and his breath connects him to the aspect of Tumah (impurity). On the flip side, if a Rosho sighs out of regret for his sins, this is a good thing because it comes from yearning for holiness, hence connecting him to holiness. The breath is the essential animating force of a person, therefore it has incredible power to either push one towards Kedusha or Tumah. From this, Reb Nachman says we should often sigh over our lowliness or our various sins, in order that we should connect to the aspects of Kedusha.
The Baal HaTanya in Likutei Amarim Perek 39 speaks on the inyan of the difference in spiritual levels between Malochim (Angels) and Tzaddikim. The Tzaddikim are on a higher level than the Malochim since Tzaddikim have to work to serve Hashem, and their neshomos dwell in the level of Briah, whereas Malochim dwell in Yetzirah, they also don’t have any Yetzer HaRa and only can serve Hashem.
Considering the idea that when a Yid makes t’shuva and repents of their sins they become a Tzaddik, we can bring these separate Torahs out to a unified whole. Rather than viewing t’shuva as simply removing sin, it is clear from Reb Nachman that t’shuva with sighing and genuine regret connects a Yid to the thread of life and holiness, bringing these influences into him. From this state, one can utilize this new influx of Kedusha to be invigorated in serving Hashem and grow spiritually. The ikar, the key thing, that allows us to become holy and grow closer to Hashem is the battle with our Yetzer HaRa, which makes us even higher than the Malochim themselves. Reb Nachman says in another place that the whole purpose of a Jew is to reign over Malochim, we can see that through our labor and seeking Hashem we can ultimately reach the level that our souls inhabit a higher realm than their existence in the first place.