The 4820 and 4821 are based on the Scania truck chassis. The old 3880 was based on a 1990s Mercedes Benz.
Of the current vehicles, the police estate is based on the VW Passat. The older police car was based on the BMW.
The small 4x4 fire car and vet's 4x4 are based on the Toyota Rav.
The little city car is based on the Smart.
Playmobil uses very subtle hints at the source of a vehicle, maybe no more than the general shape and the radiator grille, as was the case with the older police car.
Edit: I'll find some pics to support these in the next week or so - I'm a bit pushed for time currently.