From the PDG (https://pdg.lbl.gov/2008/listings/s031.pdf & https://pdg.lbl.gov/2010/listings/rpp2010-list-Ds-plus-minus.pdf) the branching rate for strange D mesons to tau leptons is about 3 orders of magnitude greater than that for D mesons. Why is this? I've thought of a few things, but I'm not completely confident.
The Ds mass is slightly larger than the D mass, and this means that it can produce a pion as well as a tau. The lighter D meson can't do this, so I assume what must happen is that the c quark turns into a d quark through the emission of the W boson, and this d quark annihilates with the remaining antidown quark in the meson to give photons. Because this is an electromagnetic process, it is slower than the strong process in the Ds. It also involves c to d and is Cabibbo suppressed.
My second thought is related. The Ds meson could also decay in this manner, except now the c quark could turn into an s quark, which can then annihilate with the anti-s. This is Cabibbo favoured.
Are these valid reasons, and is there more to be said?
References if link dies:
Nakamura, N.; et al. (Particle Data Group) (2010). " D± s" (PDF). Particle listings. Lawrence Berkeley Laboratory.
Amsler, C.; et al. (Particle Data Group) (2008). " D± " (PDF). Decay modes. Lawrence Berkeley Laboratory.