My theory is that Legendary Super Saiyan is caused by having a tail upon first transforming into a Super Saiyan. I also believe Super Saiyan 4 to actually be an evolution of that form, which would technically make it Legendary Super Saiyan 2, not a continued evolution of the previous 3 Super Saiyan states.
There isn't much evidence for this theory, it's mostly my headcanon. There is a little though. There is no mention of cutting off a Saiyan's tail being a viable tactic before Yajirobe cuts off Vegeta's tail, even counting any random stories by Vegeta and such. Thus, I find it highly likely that any previous Super Saiyans, such as the one that destroyed the original Saiyan homeworld 1000 years ago, reached Super Saiyan with their tails. Since that Super Saiyan is known to have possessed the Legendary form, the tail being the main factor just makes sense to me. Old Kai was also aware of SS4, so once again, the whole thing just kind of fits to me.
Oh, here's some fun stuff about Old Kai. He is over 75 million years old, and for much of his life he was imprisoned in the Z Sword. The "Original Super Saiyan" that destroyed the Saiyan homeworld was from 1000 years ago. That means he's not actually the first Super Saiyan, as they must have existed for 10s of millions of years at least, likely making them some of the oldest beings in the universe. Saiyans also must have had working space travel before their planet was destroyed, (or they can breathe in space) as they hadn't yet met the Arcosians, so they didn't have Planet Trade tech. That means they had to migrate to Planet Plant on their own.
I don't think it's actually possible with the information we have to determine how powerful LSS is. We don't know Broly's base power level at the time of his first battle with Goku and the Z Warriors, thus we don't have enough data to know for sure. I don't believe the transformation is inherently more powerful than Super Perfect Cell. I believe it was Broly's Zenkai that he got from losing to Goku that pushed him past the level of SS2. I think if Broly from his first movie fought Super Perfect Cell he would have been greased, but I think Broly after the first movie was stronger than Cell.
I see no reason why his normal Super Saiyan form should be any different, unless there is information that says otherwise.