When out on the road & using a prayer direction app, which opinion does Chabad use to determine the direction of Yerushalayim?
Accepted Chabad practice appears to follow the Rhumb Line bearing.
This matter is a Machlokes Achronim. In Shulchan Oruch (Orach Chaim 94:2), the Alter Rebbe describes the exact calculations to make, and these appear to conform to the Great Circle Bearing (see Simas Ayin page 5 onward, Kovetz Yagdil Torah volume 6 page 52 onwards). In the Siddur (D”H Bitfilas), the Alter Rebbe gives approximate bearings towards Yerushalayim for Northern European cities (150° SE), and although they don’t exactly conform to either bearing (see Simas Ayin for a proposed explanation for this discrepancy), it is closer to the Great Circle Bearing than the Rhumb Line bearing (if we assume the Alter Rebbe is focused on Poland/Lithuania/Belarus).
Despite this, 770 follows a Rhumb Line bearing (as observed in Kovetz Yagdil Torah) and this seems to be the widespread practice among Chabad. (To use some extreme examples, both Honolulu and Anchorage need to face West using the Rhumb Line bearing, but would need to face North using the Great Circle bearing.) It may also be observed that the Alter Rebbe’s calculations were for Northern European cities, where there is generally not much of a discrepancy between these two types of bearings.
Either way, the Alter Rebbe in his Siddur was satisfied with providing very rough approximations (150° SE for all of Northern Europe) and did not mandate any further precision. This would imply that one does not have to face Yerushalayim at an extremely precise angle, but just its general direction.