This is an very interesting grammar point.
I just want to know how native speakers think about this.
The Past Continuous with words such as "always" or "constantly" expresses the idea that something irritating or shocking often happened in the past. The concept is very similar to the expression "used to" but with negative emotion. Remember to put the words "always" or "constantly" between "be" and "verb+ing." Source
She was always coming to class late.
He was constantly talking. He annoyed everyone.
I didn't like them because they were always complaining.
Like "used to" and Simple Past, "would always" expresses the idea that something was an old habit which stopped in the past. It says that an action was often repeated in the past, but it is not usually done now. Unlike "used to" and Simple Past, "would always" suggests that someone willingly acted that way and sometimes expresses annoyance or amusement at the habit. It also often suggests the habit was extreme. To express the opposite idea, we can say "would never" to indicate that someone never did something in the past, but now they do. Source
She would always send me strange birthday gifts.
Sam and Mary would always choose the most exotic vacation destinations.
Sally would not always arrive early to class. She came late once or twice.
Ned would always show up at our house without calling first.
Mindy would not always walk to school. Sometimes, she took the bus.
Christine would always come late to the meetings.
Jeff would never pay for drinks when we went out together with our friends.
My question is that: is there any difference between "was always doing something" & "would always do something"?