The difference between 120 volts and 220 volts, is the electrical pressure; higher voltage creates more pressure. Electrical Pressure is measured in Watts of Power. 

Volts x Amps = Watts
120v x 5 Amps = 600 Watts
220v x 5 Amps = 1100 Watts (more powerful than 120v x 5 amps = 600 watts)

When applying voltage for use in an Electrolysis HHO Generator, we strive to keep the Plate voltage at or close to 2 volts. Lower voltage increases the Operating Time for producing HHO; it also reduces the amount of HHO generated. Higher than 2 volts reduces Operating Time for HHO production, and increases HHO production. So, Voltage becomes a Heat factor that must be considered. We want our Generators to operate efficient so that the plates do not get hot. To do this, we keep the voltage at, or close to, 2 volts (DC).

If a 12 volt battery is the power source, we can reduce the voltage to the plates by adding Neutral plates between positive and negative. 

+  -  = 12 volts between the plates.
+ n - = 6 volts between the plates
+ n n - = 4 volts between the plates
+ n n n - = 3 volts between the plates
+ n n n n - =  2.4 volts between the plates
+ n n n n n - = 2 volts between the plates    

In the last configuration, above, it took 5 neutral plates to reduce the 12 volts to 2 volts between each set of plates. This configuration, + n n n n n - , consists of 7 plates in Series. Amperage that passes from negative to positive, passes through each set of plates. That same amperage makes HHO between each set of plates. The electrical pressure is 2 volts between each set of plates. The number of neutral plates is what is reducing the voltage. The amount of amperage passing thru, is what is creating the HHO. It is also what is creating the Heat. 

Faraday tells us that 1 amp will make 10.44 ML of HHO between a set of positive and negative electrode plates ( + - )

He also tells us that 1.24 volts is the least amount to use (when using battery acid as the electrolyte). Higher voltage produces heat.

KOH minimum is 1.67 volts; NaOH minimum is 1.69 volts. Because there are so many variances, I suggest using 2 volts as the established plate voltage; a good goal to reach for. Your Generator will operate for long periods without overheating.

So, what does all of this information do to answer your question?
It tells us that a 220 volt Inverter will need twice as many electrode plates -- in series -- as a 110 volt Inverter.
It also tells us that the 220 volt Inverter will be capable of producing twice as much HHO.
If you want to produce a lot of HHO, 120 volts can do it. But if you want to produce even more 220 volts will do it. And, 330v, and 440v.

 The problem with using Inverters:
Inverters take DC voltage and change it to AC voltage. That requires amperage.
In the picture below, an Alternator is supplying 13.5 vdc, at 88.89 amps (1200 watts) to an Inverter.
The Inverter is changing that to 120 volts rated at 1200 watts, that can handle a load up to 10 amps.

120 volts, would need 61 plates in series to have plate voltage at 2 volts. It will need 10 amps to produce 1200 Watts and 6.264 LPM.
A 12 volt generator would need 10 sets of 7 plates in series, each drawing 10 amps (100 amps total), to produce 1200 watts and 6.264 LPM.
A 220 volt generator would need 111 plates in series at 2 volts, and 5.455 amps to produce 1200 watts and 6.264 LPM.

Bottom line is, it takes power to make HHO. And it takes power to make voltage. If you use an Inverter on your 12 volt power system, it is going to draw more power from your alternator than you thought it would. The same can be said for DC to DC Converters. In the long run, from the alternators view, I think it is best to just work with the power source you have.