Interesting question! When you say "chord-leading," do you mean "voice-leading" or "chord progressions"? Voice-leading is controlled by the chord progression, so I suppose the rules of the one inform the rules of the other. But my answer, in short, is this: the chord progressions of the modes may differ from one another, but voice-leading rules will probably always stay the same.
In the Ionian mode, the music usually continuously reaffirms the tonic, which is accomplished most powerfully by use of the dominant seventh chord. In the dominant seventh, the double half-step motion combined with the root motion of a fifth is what causes the ear to be drawn inexorably back to the tonic chord. For example, in the key of C major, the dominant seventh chord would consist of G-B-D-F. When the chord resolves back to the tonic, the B moves a half-step back to C, the F moves a half-step back to E, and the G moves a fifth down to C.
The question, I think, is whether we expect this sort of dominant-tonic relationship (and other similar chord relationships) to apply in other modes. From my own experience, it seems much harder to accomplish the reaffirmation of "tonic" because of the lack of half-step motion. Certainly, one can still utilize the root motion of a fifth to add a sense of final resolution, but it's not nearly so satisfying without the half-step motions (for whatever reason) as in the Ionian. In the Dorian and Mixolydian modes, for instance, one can just as comfortably resolve to the tonic from the dominant as from the subtonic chord.
However, the rules of voice-leading still apply, regardless of the mode. It is generally bad form to use parallel fifths, fourths, and octaves; or to use cross-voicing; or to double pitches other than the root of the chord excessively; etc. It is just as easy or difficult to avoid these problems in any other mode as it is to avoid them in Ionian mode. For instance, it's always a good idea to have a leading tone resolve to its upper neighbor. In Dorian mode, the leading tones fall in different places functionally than in the Ionian mode, but it's nevertheless bad form to use them in such a way that they fail to resolve to their upper neighbor. As always, one can break the voice-leading rules to accomplish a certain effect, but in general, they seem to apply in all modes.