The major similarity between these two riots is that both expressed the desire of the people of Singapore to have more control of their government and society. The people wanted to throw off the control of the Europeans in the years after WWII.
On the face of them, the riots have little in common. The Hertogh riots had to do with religion while the National Service riots had to do with politics. However, in a sense, they were both about who should run Singapore. Both riots can be seen as demands for local control. The Hertogh riots can be seen as a demand for more respect for local religions and for local people (rather than British courts) to be able to be in charge of justice. Similarly, the National Service riots can be seen as a demand that the British should not be able to force service from their subjects.
In both cases, the riots center around the issue of who should control Singapore. They can both be seen as demands for local control and an end to colonialism.