Eevee world probe is not suited for very high frequency details and even less for sunlight. For this we want to introduce a threshold. All light under the threshold would be pushed to the world diffuse/reflection probe. All light above the threshold would be moved to an importance sample map and used to position a (virtual) sun light that represent the missing energy from the probe.
We can position the sun in 2 ways: randomly per sample using the importance map, or fixed using a Spherical harmonic decomposition.
The first one offers more precise lighting (can work with multiple light source) when the second one offers more stable lighting (good for a sun).
The good thing is that this virtual sunlight can be shadowed! Thus making most of the light coming from the environment shadowed.
This should fix this sort discrepancy between cycles and eevee:
Estimate : 2 weeks