That means cars require one extra component and an extra conversation of energy which trains don't need.

Well, tbf, both trains and cars require converters (i.e. inverters like variable frequency drives or VFDs; or rectifiers) to match power between the local electric supply and traction motors, in the case of trains, or between the battery and traction motors, in the case of cars.

You need to be able to ramp up or down voltage or current (or both) depending on the drawing load that the motor sees at each and every moment of a trip (cars and trains). Then there is the possibility of your train jumping between different electric systems along its route, and so you need to have a way to accommodate those difference if you want to serve the most amount of passengers.

There are Battery Electric Multiple Units (BEMUs), too, out in the wild today that incorporate batteries in addition to electric service on trains (or just batteries alone), mostly in Japan and some in Europe. These are in the minority though compared to electric-supplied units.

Interestingly, there are some projects, most notably in Germany, where overhead lines are being introduced to trucks, fuzzying the differences in transportation modes even more.

I still get your point about the conversions, though. Batteries don't have 100% Coulombic/Faraday efficiencies, meaning that they don't charge up from 0-100% every charge cycle: you might start at 0-100%, but the next charge cycle might be 0-99.9999%, then 0-99.99%, then 0-99%, etc. This efficiency loss isn't as great as the other losses you might find in the converters previously mentioned, or other resistive losses such as via Eddy currents in the motors/axles, demagnetization of the motors, etc.

Trains use: power lines -> electric motor Cars use: power lines -> electric battery -> electric motor

A better description of these processes would be:

Non-BEMU Trains: power lines -> converter -> electric motor (acceleration)

Non-BEMU Trains: electric motor -> converter -> power lines (deceleration)

Cars/BEMUs: power lines -> converter -> [battery -> converter -> electric motor] (charging [acceleration])

Cars/BEMUs: [electric motor -> converter -> battery] -> converter -> power lines ([deceleration] discharging)

Furthermore, bigger machines can be built to be more efficient than smaller ones. So bigger motors can use (electric) fuel more efficiently than smaller motors.

Totally. And trains that add batteries onboard can reduce the advantage that non-battery EMUs have, moreso resembling locomotives with big diesel engines and fuel tanks. I still find BEMUs better though because you can run the trains as married units, just like EMUs (and I suppose DMUs), but batteries can also be distributed along the rolling stock to allow for greater weight balancing. Idk if the major manufacturers like Siemens or General Electric have plans to design systems this way, but greater adoption may lead to more varied designs.

Hope this helps the discussion!