The main take away from the second is that the early Wittgenstein was about trying to show the limitations of thought. The later Wittgenstein went deeper into the same challenge. Though the tractatus is an eternal philosophical classic, I personally think the later Wittgenstein was more interesting. Mind you – that is based solely on these two books, not on reading the relevant literature myself.
The thing is, the later Wittgenstein faces up to what is now much more a common insight: that the ambiguity of language is not going away; That the way we put things into words changes how we deal with them; That math is an instrumental science, not a truth finding one etc.
The biography shows Wittgenstein a troubled human being, as most geniuses are. The subtitle ‘The Duty of Genius’ refers to the deep obligation Wittgenstein felt to BE a genius. In fact, he only decided that his life was worth living when Bertrand Russell adopted him as his disciple. This says something rather terrible about Wittgenstein’s childhood environment. Not for nothing did several of his brothers commit suicide.
As an Austrian living through both world wars Wittgenstein’s life also turns into a unique look at the Europe of that time. This is true also of the Heidegger biography by Rudiger Safranski btw. (I read that one in Dutch). [This: Martin Heidegger: Between Good and Evil is probably it, though the title is rather more dramatic in English than in either Dutch or French, for example]