You're right. If you say
El avión es más grande que el carro
it seems that you're stating that a specific plane is bigger than a specific car. Yes, sometimes the singular will be valid, as in the following example:
El hombre es más inteligente que el mono
This case works because "el hombre" can be understood as "the human race". Nonetheless the use of the singular can lead to misunderstandings. In order to make the sentence applicable to any plane and any car, just write the sentence in plural:
Los aviones son más grandes que los coches
Another way to achieve this is to use the indefinite article:
Un avión es más grande que un coche
Note: I used coche because in Spain we don't use carro with the meaning of "car".