Solar are violent releases of solar magnetic energy. Other stars are also known to have magnetic fields, in some cases much stronger than the Sun. How do the largest stellar flares compare to the largest solar flares in terms of energy released? It would also be interesting to normalize the answer by the strength of the magnetic field to be able to compare the efficiency of magnetic energy release on other stars compared to the Sun.
This is a part answer, a comparison of sun-like star superflare behaviour with our sun.
According to the article Superflares on Solar Type Stars Observed with Kepler I. Statistical Properties of Superflares (Shibayama et al. 2013), observations were made on solar-like stars (type G), over 500 days.
One key observation was that they
found 1547 superflares on 279 G-type dwarfs
Despite this seemingly massive amount, they deduced that
the occurrence frequency of superflares with energy of 10^34 − 10^35 erg is once in 800-5000 years.
in some G-type dwarfs the occurrence frequency of superflares was extremely high, ∼ 57 superflares in 500 days (i.e., once in 10 days). In the case of Sun-like stars, the most active stars show the frequency of one superflares (with 10^34 erg) in 100 days.
These are associated with very large star-spots, far larger than those on our sun.
There was an earlier theory that the presence of Hot Jupiters were a major contributor to super flares, hence the reason that our Sun did not exhibit this phenomenon often. However, there is some evidence of a possible past superflare occurred from our Sun:
an occurrence of a energetic cosmic ray event in 8th century recorded in a tree ring of Japanese cedar trees. There is a possibility that this event was produced by a superflare (with energy of ∼ 10^35 erg) on our Sun.
and no hot Jupiters were detected around many of the stars observed either, so this theory is largely ruled out by the authors. Rather, they postulate that G-type stars 'store' magnetic energy.