question

You haven't given us enough information to say which is "better." The latter system is objectively bigger. Is it big enough for your needs?

The "100A autotransformer" is really only a 32A effective device. If you can have more than 32A of imbalance in your house loads L1 vs L2, you will need something else (a bigger autotransformer, multiple autotransformers in parallel, multiple 120V inverters in split-phase instead), or you will need to accept the shutdowns that happen when that imbalance occurs.

I would be concerned that your installer is not asking you these basic questions first. Have they done this before?

You most likely want the second option with a 240V Quattro, for the following reasons:

(1) Most high power home loads are 240V, not 120V. With the 240V Quattro, these draw directly from the Quattro - no current flows through the transformer. You can take the full 15000VA output from the Quattro at 240V, which you could not do (not even close) with the first option.

(2) In a well-organized distribution panel, 120V loads are intelligently split across the two phases. Depending on how you use 120V loads, the current to the neutral connection may largely cancel out, and will be small compared with the total current you are drawing from the 120V lines. The reduces the burden on the autotransformer, and improves the regulation of the 120V lines (keeps the two sides in better balance). Remember, the transformer limited to 28A continuous neutral current, so the 120V loads on the two phases can not be more out of balance than that.

To add some more: thinking about this further, I note that the Victron autotransformer weighs 12.5 or 13.5kg (for the 32A and 100A pass-through models, respectively).

So we could guess that the toroidal autotransformer itself weighs at most 11-12kg. For such a size transformer with a 240V total voltage, one would expect the total winding resistance to be of order 0.35 Ohms, looking at online data for similar devices. The rating allows for 28A max. continuous neutral current, which, with the resistance previously estimated, would lead to the neutral connection departing by 0.35 * 28 / 2 = 5v from the mid-point of the input (240V) lines at max. neutral current (for a resistive load), which is relatively poor balance (one side 125V, the other 115V). This does not include any contribution from leakage inductance.

Put another way, if you are using a 15000VA inverter, you will likely not be happy with the neutral balance achieved. This autotransformer is simply too small for this sort of power level. You would likely need to parallel a couple of units, assuming they are appropriately matched.

Alternatively, you can probably buy a larger transformer of suitable characteristics to serve in this application.

Sorry, my bad, lost a factor of 2 somewhere (autotransformers can be tricky devils). 5V is the *difference* between the two outputs, so one would be 117.5V, the other 122,5V at 28A neutral current (remember, this is just a guesstimate, as Victron have not given us any data pertaining to regulation).

So the balance is not that bad, but not wonderful either (and that's before we add reactive effects).