Objectively, measuring by mass is going to be the truest most correct, accurate, and all around "best" way of determining "how much muchness" there is to a thing. You can measure it in liters, or pounds, or you can measure it by the number of McDonald's straws it fills up or how many seconds it takes to drip through a sieve. But all of these are subjective. Your sieve might have a finer mesh than mine, McDonald's in different countries might not use the same straws, things weigh a lot more pounds on Jupiter than they do on one of its moons, and "ten liters of H2O" doesn't say much when you don't know if I'm talking about steam or ice. But if you know the mass of it, none of these things matter. Mass is mass. One gram, is one gram. It doesn't matter if it's on Jupiter, or if it's vaporized, or how big your straws are, and maybe it's a solid lump and won't even go through a sieve, but if you can manage to figure out what something's mass is in the here and now, you know it will have that same mass in the then and there.
Fortunately, here on the earth's surface, where we all experience roughly (to a very very small fraction) the same gravitation, mass and weight are intertwined through the gravitational constant, and a properly calibrated weighing device (such as an electronic scale with digital readout) can give a very precise and accurate representation of an object's mass. Therefore, objectively, measuring by weight is without question, the superior method. At least in the presence of a constant gravitational field. It probably wouldn't work out so well for those guys on ISS, but I don't think they're allowed to vape.
In the real world, though, none of that really matters. Sure, pouring our ingredients through a sieve is a horrible way to measure by any account, but the rest of them are legit. I mentioned before that we all experience roughly the same gravity. Well, we also experience roughly the same atmospheric conditions, and this, combined with the fact that liquids in general just aren't very compressible anyways, means that the volume will be relatively consistent in all foreseeable circumstances, as well. You want to measure in gallons, or liters, or cups or spoonfuls or Coke-bottle caps, be my guest. Counting the number of straws it takes to hold it is essentially just the same as "measuring by length" in a shape with constant cross-sectional area. Well, we've already got a name for that, it's called a graduated cylinder. Some of them have pumps and interlocking nozzles attached, and we call them luer-lock syringes with graduated markings.
They work "fine." There's nothing "wrong" with them. The digital readout on the electronic scale is nice, but if you have good eyes, a steady hand, and quality, calibrated equipment you can probably measure as accurately and precisely, and both ways can likely be more accurate and precise than any of us can taste, anyway. So in the real world, it all comes down to personal preference. There is something to be said for the ease of cleanup (or rather, lack of cleanup) involved when you can have all your ingredients in dropper bottles and mix directly into the container atop a digital scale, but some people are just more comfortable with the idea of using volumetric measurements. And that's okay. You can get plenty good enough results measuring liquids, by volume, under relatively consistent environmental conditions. It's absolutely "fine" if you prefer to do it that way. The theoretical flaws are slight, and not likely to make any difference in real-world application. Objectively, though, there is a "best" way, and those people are technically doing it wrong.