It would be a much different story if British English and American English had different words for "a car". Which, by the way, happens in Spanish dialects ("el coche" vs "el carro").
but if you showed an argentine a picture of a car, they might very well say 'auto' while perhaps someone from elsewhere would say 'coche', leading to a basically incorrect point of difference being measured in this study between the two dialects
You can design a study with a high level of data granularity. You could even track differences in pronunciation and grammar if you wish so.
A well-designed study, in my mind, would compare the usage of a varied bag of words. Starting from articles, pronouns, numbers, common verbs, then common objects, verb forms, less common adjectives, ending with uncommon objects and phrases. The compared words would be weighted based on their frequency. If two dialects have the same articles, pronouns, numbers, etc. and some differences in less frequent nouns, they would be similar rather than radically different - at least lexically. Things might look differently if we look at pronunciation.
I don't know what list of words was compared in the study linked in this subthread, so it's hard for me to say anything about it.
* auto: car
* coche: stroller or carriage (depending on context)
* carro: cart or carriage (see above)
Automóvil: Formal word for car.
Coche: Car. If used with 'de caballos' (of horses), well, carriage.
Carro: Carriage, or trolley.