We have an equivalent - League 1. The only difference to managing Real Madrid Castilla and someone in League 1 is that at Real Madrid Castilla there isn't a playing budget to work with. In both situations the manager is responsible for picking the team, choosing the players, motivating them and working on the tactics.
There are plenty of top level clubs where the manager, or head coach, doesn't have much say in transfers.
Actually has nothing to do with that, there is no comparison in this country because no club in league 1 has the comparable club structure of Real Madrid etc (which accounts for a great deal)
The likes of Leeds, AV and numerous others have suffered recently because of the issues above the managers head.
Of course just because the board is successfully running the "A" team as it were, doesn't automatically mean it will work for the team lower down but it takes a lot of pressure off (not to mention the scouting etc etc and the name of the club itself will make it easier to attract the "right " players.
IMO that is a huge difference.
In regards to the Bradley decision I still think its incredibly bizarre , but maybe the fact that Giggs has been quoted as saying that he was getting mixed messages from the owners and the management as to why he is seemingly not that bothered about losing out (from the couple of different clips Ive seen of him talking about it)