Update(column) merely states that column participated in update, but not that its value has changed. For instance,
update Person SET Name = Name
yields true in update(name) even though Name has not been changed in any row.
To check if new values differ from old ones, you would employ except because except will remove rows from top set that exist in bottom set. As person table probably has primary key there is not a danger of removing changed item that has a counterpart in deleted. However if you decide to change *
to a list of interesting columns be sure to include primary key.
insert into logTable (ID)
select a.ID
from
(
select * from Inserted
except
select * from Deleted
) a
Added benefit is that this works for inserts too because Deleted will be empty and all rows from inserted will be returned.