When you planned the routes in MRA, did you make sure you had the Here (Garmin) maps selected?
Garmin devices use Here maps, so if you planned them in MRA with a different map the device could calculate the route differently when you transfer them.
You can also transfer routes directly from MRA to a Garmin on Windows or Mac using the built in connector, this bypassing Basecamp. However, you could still suffer from the routes recalculating differently if you don’t use Here maps in MRA.