Gerund phrases describe continuous or ongoing action, or action that happens at the same time as another action. Past-tense verbs generally describe a completed action, or a sequence of actions.
Closing her eyes, she thought about her life.
This means that she's thinking at the same time as she closes her eyes.
She closed her eyes and thought about her life.
First she closes her eyes. Then she thinks.
It's not so much an "effect" as it is "describing actions in the order they occur."
In your second example, you have two problems.
1) Being so confident and handsome is more of an adjective phrase. Being is not acting as a gerund there.
2) You have a dangling participle. The subject of first clause is "him," but the subject of the second clause is "women."
It should properly read
Being so confident and handsome, he drew women to him.
(separately, vultures surround dead, rotting things to eat them... is that the image you were going for? Because seriously, eww. Is he a handsome, confident zombie?)