Advantages of DDS over arbitray function generator
They are the same thing. A DDS generator without arbitrary waveform capability will have a fixed waveform lookup table stored internally. A DDS generator with arbitrary waveform capability will have a programmable lookup table.

A DDS generator without arbitrary capability is a little cheaper, but these days the difference is quite minimal or in some cases non-existent. The difference in pricing of test equipment is mostly historical, i.e. they can charge you extra for the arbitrary waveform function.