I agree with Dyson that the main difference between 'birds' and 'frogs' is that while frogs tend to focus on their particular domain solving problems, birds try to find and bring in connections between areas which can open up a much bigger new area of problems to solve. However to me this way of looking at things is almost dependent on your philosophical outlook on mathematics. Do you view mathematics as fundamentally one big area similar to how fundamental physics has their theory of everything? Or is it just collections of various problem solving strategies grouped by likeness? I find Tim Gowers' equally famous essay on the "Two Cultures" of mathematics[0] quite relevant here. Particularly of relevance is how some areas of mathematics, especially those of the algebraic kind, are more "structural" compared to a subject like combinatorics (on the surface this would make obvious sense because algebra broadly studies structure). I can't speak to being an expert on the past 50 years in mathematics but it would seem to me that these structural areas of mathematics have 'dominated' so to say pure mathematics in that time period. One thing however I would like to point out is going into the future how is the split between so called birds and frogs going to be? Most mathematicians or physicists or even academics more broadly will always be frogs because to be a bird you need to have frog like depth in several areas before you can start making connections between them. However as subjects get more specialized you would expect that slowly the amount of birds will become less and less because the amount of knowledge required will become higher and higher.
[0]: https://www.dpmms.cam.ac.uk/~wtg10/2cultures.pdf