One street stops. The other never does. Below, Oak St. has the stop signs and Main St. is the through street. Pick a scenario to watch the legal right-of-way play out — a green ring means that driver may proceed, a red ring means they must stop or yield.
…the driver of a vehicle approaching a stop intersection indicated by a stop sign shall stop before entering the crosswalk on the near side of the intersection, or if there is not a crosswalk shall stop at a clearly marked stop line; or if there is not a crosswalk or a clearly marked stop line, then at the point nearest the intersecting roadway where the driver has a view of approaching traffic on the intersecting roadway. After having stopped, the driver shall yield the right of way to a vehicle that has entered the intersection from another highway or that is approaching so closely on the highway as to constitute an immediate hazard during the time when the driver would be moving across or within the intersection.
Excerpt. Full text: MCL 257.649 — Michigan Legislature
The driver of a vehicle within an intersection intending to turn to the left shall yield the right of way to a vehicle approaching from the opposite direction which is within the intersection or so close to the intersection as to constitute an immediate hazard; but the driver, having so yielded and having given a signal when and as required by this chapter, may make the left turn and the drivers of all other vehicles approaching the intersection from the opposite direction shall yield the right of way to the vehicle making the left turn. …
Excerpt. Full text: MCL 257.650 — Michigan Legislature