Relative directions in teleport are relative to player targets rather than executer.

Teleporting (teleport NOT tp) an entity to another entity uses the relative co-ords of the executer, but the rotation is relative to the target. This is not the expected result.

execute @e[type=armor_stand,c=1] ~ ~ ~ teleport @p ~ ~ ~ ~ ~

teleports the player to the armor stand but does not match the armor stand's rotation.
Example: Thanks to OSX

Further note, thanks to SirBenet:

execute @e[type=armor_stand,c=1] ~ ~ ~ teleport @e[type=pig,c=1] ~ ~ ~ ~ ~

teleports the pig to the armor stand with correct rotation, so it seems to be more of a player thing.

Another example from OSX