The two you mentioned are bad, because they implicitly shift the fault on the person on the receiving end, because they make qualifying statements about the person without addressing your own actions that led to it at all. Very similar to the badness of "I am sorry you feel that way about what I said", because it only addresses the person on the receiving end and makes it sound like there is something wrong with them.
"I regret that my actions had this effect on you" is not bad because it doesn't do that. It clearly just says that you are sorry for your actions causing such an effect, without making any qualifying statements about the person on the receiving end, leaving the possibility of your actions being wrong fully open.
The two you mentioned are bad, because they implicitly shift the fault on the person on the receiving end, because they make qualifying statements about the person without addressing your own actions that led to it at all. Very similar to the badness of "I am sorry you feel that way about what I said", because it only addresses the person on the receiving end and makes it sound like there is something wrong with them.
"I regret that my actions had this effect on you" is not bad because it doesn't do that. It clearly just says that you are sorry for your actions causing such an effect, without making any qualifying statements about the person on the receiving end, leaving the possibility of your actions being wrong fully open.