Both can be used in different situations, I can only show you by example sentences [emoji] 又驚又喜: feel shocked, and happy at the same time 一邊吃飯，一邊看電視: eating, and watching TV at the same time

又又 is usually used to describe two concurrent situations/status/conditions/mood of something/someone. 听到这个消息，我又兴奋又紧张 (to describe my mood)；外面又刮风又下雨 (to describe the weather situation)，别出去了；上了一天课，我又饿又累 (to describe the health condition)。 一边一边 is quite neutral, simply refers to two actions happening at the same time. 他一边吃饭一边看电视；他们一边上课一边聊天。

I will probably say 又...又 usually link adjectives together , 一边 ...一边 usually link to actions together(examples seen in the first comment) Compare to 外面一边在下雨，一边在闪电, 一边吃饭，一边看电视 is a more common way of using 一边 ...一边

Yea, both can be used to indicates events/actions/feelings pairs that happens at the time. 既。。。又 works the same way too. However, be careful with 一边。。。一边，because besides indicating timing, 边 can also be referring to locations(sides). For example， 外面一边在下雨，一边在闪电。 If the speaker is referring to timing, then it means it rains and lightnings at the same time. However, if the speaker is referring to the locations, then it means on one side, it is raining (only), and on the other side, it is lightning (only). hope it helps : )