DW and I started off by being frugal (but not cheap). As others had done, when we married we only lived off of one salary and tied our spending to that. As our income grew, we increased our lifestyle - but at a MUCH lower rate than our income growth. For example, a salary increase of 5% might only raise our spending budget by half a percent, if at all. If I received a bonus, we might splurge no more than 20% of it and save or invest the rest.
As we built up savings and then started to invest, I realized early in those personal finance years that I did have the time, patience, or knowledge to try to beat the market. I settled, in baseball terms, for trying to just make contact and hit singles instead of swinging for the fences. One result was shifting away from individual stocks into mutual funds, then index funds and index ETFs.
One result of combined savings and investing is that we don't need to try to beat the market to have a good financial year. We are happy to lessen our investment risk as we are still able to save 30-35% of our income (and in some years even more). In fact we have cut down our savings this year to spend one some hopefully one time home renovations, but should still end up saving at least a quarter of our income. Then we just invest a portion of that income in a diversified manner.
So I don't see it as being a "versus", for us starting with savings, then doing both in a balanced manner allows us to invest at the level of risk we are willing to take and still sleep at night. That helps us look at days like today, where the market will likely take a pounding, and not worry.