I think you get the basic differences. With VTSAX you say "I want to buy $x worth of shares at the next closing price," and you can put in the order whenever you like. If you want to harvest losses and move your money into VFIAX to avoid wash sales, you can even say "trade all my VTSAX for VFIAX at the next closing price."
With VTI you have to log in during market trading hours and say "I want to buy N shares for no more than $y each" (if using a limit order), monitor your order to make sure it gets filled, adjust your limit price as needed, etc. If you want to exchange one fund for another you need to wait for the sell order to get filled and then repeat the process with the buy.
As you may have guessed from the way I phrased it I happen to prefer the mutual fund version for the simplicity, but to each their own.