I have both FAA and EU licenses and have flown Juraissic and NG versions of the 737.
Having first-hand experience of the various makes and models as well as the US and EU licensing authorities, this is how it works:
In the US, no matter which type of 737 you take on your checkride, you will only ever see a "B737" type written on your certificate. Thus, it is not evident from the certificate alone, which model the training/experience was gained on.
In Europe, you will - B737-200, B737-300/400/500 (considered classic nowadays) and B737-600/700/800/900 (Next Generation).
With regard to Boeing, on the NG models, the overhead panel was kept similar to earlier versions by continuing to use toggle switches instead of the push buttons that are featured on the 747-400/757/767/777s. The reason: to keep the same basic type rating so that pilots would only have to do a "differences" course. If they had changed the overhead completely as well as the glass, then it would have been a totally separate type rating but they wanted to keep it in the family, so to speak.
In another life, I was flying and rated on a Juraissic -200, did the differences course with Boeing and ended up flying the 737-800. Then when I decided to add the 737 type on my FAA ATP, I did a 737NG PIC Initial with all that entails and checked out in a 737-800 sim. My FAA ATP shows B737.
Hope that helps to those still wondering.
B757driver