I'm confused. The subject line of your post suggests that you're trying to choose between the two models, but from the text of your post it sounds like you're buying both of them.
Since I have no experience with either model, I can only go by their manuals.
The YPG-635 has twice the polyphony of the YDP-113 (64 notes versus 32 notes).
The YPG-635 has many more voices than the YDP-113 (503 versus 10).
The YDP-113 has much stronger amplifiers than the YPG-635 (20W x 2 versus 6W x 2).
The YDP-113 has MIDI ports, whereas the YPG-635 has a USB port.
The YPG-635 can play styles and has a built-in song recorder; the YDP-113 does not.
The YDP-113 has a more "classy wooden" look, whereas the YPG-635 has a more "modern plastic" look.
They're similar in some ways, but very different in others. Even though the YDP-113 has far fewer voices and effects than the YPG-635, I suspect that the few voices it does might be better-sounding than the equivalent voices on the YPG-635, although you'd need to listen to both keyboards to verify that. I think the YDP line is generally aimed more at pianists, whereas the YPG line seems to be aimed at keyboardists who want a piano-like feel but with arranger features as well.
If you're mostly interested in playing the piano and don't care about using styles and recording songs with a variety of instrument tracks, then the YDP-113 would probably be a more satisfying purchase-- although, as mentioned above, it has a lower polyphony.
But if you're more interested in exploring some of the features of an arranger while also enjoying a reasonably piano-like keyboard, then the YPG-635 would probably be a more satisfying purchase-- although, as mentioned above, it has weaker amplifiers.
Additionally, the YPG-635 is better-equipped for connecting to a computer via its USB port, whereas the YDP-113 is better-equipped for connecting to other MIDI instruments via its MIDI ports.