In my opinion, saving and investing are different, so we should not consider investing as a new form of saving, and only know invest and ignore saving. Remember that investing is risky, there is no guarantee that it will always be profitable. Meanwhile , saving does not help us increase our assets, even our money depreciates over time, but at least it does not make us bankrupt or lose all our assets like investing. Therefore, both are important and we should have both, not risk choosing either one .
Do you mean saving and investing should be equal? I don't think so.
Whenever people choose to have a big amount in saving, they do what with an intention for waiting a good business or project to invest, so it's always about investment. If someone already know what they should invest, better to hold savings worth of 12x monthly expenses, rest of them should be used for investment.
So if someone already have a lot of money, it could be 1% saving and 99% investing.