Rabbits are not rodents actually.
From wikipedia, rabbits are lagomorphs
they have four incisors in the upper jaw (not two as in rodents);
they will only eat vegetation (unlike rodents, who will eat meat and vegetation)
the male's scrotum is in front of the male organ;
the male organ has no bone (baculum) unlike the rodent male organ; and
they will redigest first-time droppings (called cecotropes) to obtain the most from their plant diet.
They resemble rodents, however, in that their teeth grow throughout their life, thus necessitating constant chewing to keep them from growing too long.
There are other differences that I can see:
Rabbits only live on the ground, neither on trees, nor sewers.
And the wild rabbits are cooked usually with garlic and wine or brandy and eaten with fried potatoes in Spain, and the rats only during war or blockade times.