It won't get stabler than the crystal oscillator you're using to drive it. What you can do with DDS is take a very stable (but un-pullable) master oscillator and use it to generate equally stable clocks at arbitrary frequencies. That in turn can be rolled into a digitally controlled PLL if needed. One should be on one's guard for nonrandom spuriae though, especially if the ratio between the master clock and the synthesised clock is nearly, but not exactly, simple. The plot you posted was for an exact 25:1 ratio, which is sure going to look good, but try a 25.01:1 ratio next. The noise floor would still be that of the master oscillator but there'll be all sorts of spikes sticking out. The linearity of the DAC used in the DDS is key, as is the lowpass filter.
DDS is used in the Audio Precision test sets (where it appears to function flawlessly), in the Mutec iClock, and in the Dice II (TC electronics) JET PLL, to name three.