So in the anime series we were introduced to Kale who many labeled "female Broly". Vegeta makes some comments about her possibly having "the true super saiyan" and we see her transformation with white eyes, bulky form and green hair and aura. And now we have the official version of Broly, with a transformation which in some sense looks the same, but different perhaps for artistic / animation style reasons. Are these transformations the same? Is there hard evidence that now they have the same transformations or may be now Kale and Broly's tranformations will be treated like different super saiyan transformations?
Most likely Yes. Based of the characteristics of the transformations, they seem comparable indeed. This is because the character of Kale was based off Broly. During a story conference, it was mentioned that the character of Broly was very popular. Hence, it was suggested to include a Broly like character in the Tournament of Power. This resulted in the creation of Kale. You can read more about it here.
Broly is just overall strong and tends to grow stronger at a very rapid rate during battle. Kale displayed something similar(Mainly in the manga) but obviously not to the same extent to that of Broly. However, two fighters using the same Transformations don't necessarily have to be equal in strength. Like for example, Super Saiyan Goten, is nowhere close to Super Saiyan Goku. Although, while Kale's initial Berserker form can be compared to that of Broly, she did manage to control her power into a less bulky version of the transformation. It was implied that Broly was out of control from the point he began using his wrathful form. So I think it is pretty obvious that Broly doesn't have real control over his power. Hence, it is quite possible he might once he manages to use his true power more effectively.