This is a really interesting and important question. I’m not sure there’s a dichotomy and I think that the focus should not just be on girls but on boys as well - not in the sense of getting boys more interested in STEM as they already are but in making them realise that STEM is for girls as well.
I’ve finally finished Delusions of Gender by Cordelia Fine. It’s a book I can’t recommend enough and I will be referring to it a lot, I’m sure. Anyway, the last part of the book discusses society and culture and how that shapes us from a very very early age - as soon as women know the sex of their foetus they start treating it differently, thinking that boys kick more than girls and so on. As soon as they’re born children are dressed and dealt with differently according to whether they are male or female and are bombarded with messages all around them that women and men are different. At the age of about two children are not only able to distinguish men from women and can tell what activities and attributes each sex is supposed to have, but also know which category they fall into themselves. As we are social animals, children want to conform and as they have very little to distinguish themselves at such as a young age other than their gender, this becomes the key identifier. They know which toys are ‘for girls’ and which are ‘for boys’, which clothes are for which sex, what activities are for each sex (washing up the dishes vs cleaning the car, for example) and so on. Kids who step ‘out of line’ of their gender roles are ostracised and are forced to conform through peer pressure. This much is from the book.
Where I’m going to extrapolate is by saying that if we want girls to be more interested in STEM it’s not just about making it more attractive to them but also about making it less of a ‘boy thing’ for boys. Any straying from gender norms is ‘punished’ by peers, both male and female, and it’s not enough for girls to support each other if as soon as they venture into ‘boy’ territory they are made to feel completely unwelcome and as if they are stepping into ‘enemy territory’.
This is a really long-winded way of saying that I think a combination of the two approaches are necessary. One thing the book said was that just a small amount of change (giving kids books with gender-role-reversed characters, for example) can create a change in attitudes really quickly. So the fastest way to get STEM as a subject anyone can do, male or female, may be to just make kids aware from as early an age as possible that women can and do work in STEM and not to make a big deal of it so that they’re aren’t ‘exceptional’ but are just examples of scientists. So rather than talking about ‘Watson & Crick’ we talk about ‘Watson, Crick and Francis’ and explain each of their contributions. I think maybe also focusing on teams of people rather than the lone genius would encourage more people into STEM as very few people can associate with that whereas a lot more people can imagine being part of a team and making a small contribution to a bigger whole - it’s less daunting and more achievable, plus it has the added bonus of being much closer to the reality of how STEM works these days.
I’m not sure if that entirely addresses your question but it gave me a chance to waffle about something that I’ve been increasingly aware of - that it’s not enough just to turn every woman into a feminist to make any progress, we need to convert the men as well.