Given the these two choices I would suggest Hamburg, the cultural center of North Germany.   
As suggested doing s day to Schwerin from Hamburg Hbf is quite easy,  time well-spent,  and a direct shot, much easier than from Berlin Hbf.   The famous Schloss in Schwerin is under (part of it) reconstruction but still worth seeing and not to be missed.  
Historically, if you're after that, in front of the Schloss is the large Victory Column (Siegesäule) to the War of 1870,  it is also the memorial to German soldiers from the  Mecklenburg-Schwerin grand duchy , (there were 2  duchies of Mecklenburg  prior to WW1, Schwerin  and Neustrelitz) ,   killed in that war, just as I saw large soldiers'  memorials  in France, such as in Troyes, Toul,  Epinal , to name a few  of these  sites.
In the greater Hamburg is also a site of remembrance  of  Nazi horror,  the camp site of Neuengamme, accessible by the S-Bahn.
There is a lot more Prussian-German ,  WW1 and WW2  history  in this area if you want to track them down from  Lüneburg to Flensburg, as well cultural historical sites, obviously.