According [to this wiki article][1]:

> The old series begins with the Black Swordsman arc, continuing through
> the Golden Age arc
> 
> The new series commences with the "Conviction" story arc, starting
> around chapter 115 of the manga, and introduces Puck, Isidro, Farnese
> and Serpico as characters.

So the new series picks up where the old series left off, the difference between the two is that the first series is anime drawn and the new series is primarily cgi.

  [1]: https://en.wikipedia.org/wiki/Berserk_(manga)