Higher power DPSS Lasers need larger crystals, most assuredly. They also require much larger pump diodes and precise alignment as when you get into the higher end of the power curve with DPSS you have to consider that composite crystals don't exist. Once you start dabbling in professional level equipment, expect to encounter professional level headfucks. Composite crystals are, generalisation ahead, for low powered lasers. When you start getting serious and getting quotes on separate crystals, you'll notice there is a size disparity between the NdYVO4 and the KTP Crystal on is short and fat and the other is long and thin, that is the best design for the best output, it is the reason why high power DPSS Lasers don't use composite crystals, the mismatch in the crystal sizes for the task at hand starts to exceed the capacity of composite crystals.
Aligning the diode, the two crystals, the mirrors and the lenses is not an amateur friendly task. Add to that the need for a serious <600nm cutoff filter (to remove the pump & the IR from the NdYVO4 will save your eyesight, 808nm diodes are underrated in the permanent damage they can and will do to the unprepared, once they get into the multiple watt category, they are capable of blinding, completely & permanently rather rapidly).
Then you could get really excited and start attaching multi-Watt 808nm Pump Diodes to a multiplexing arrangement, with the concept being to output the lot into the back end of a crystal, this is seriously a job for professionals (they don't need degrees, just commonsense and a knowledge of what the fuck they are doing). Finding large enough crystals to allow for them to be pumped by 100W of 808nm Light and output in the 10W Green range is my personal dream (one day).