I don't have any personal playing experience with cone chests.
What I do know is that such a chest has one groove
per stop (instead of one groove per note). Therefore, you've got a certain amount of blending between different notes of one stop, rather than between different stops for the same note. One consequence is that by putting lots and lots of 8' stops of different intensities into each division, the (relative) lack of per-note-blending allows to achieve a crescendo through progressive addition of these stops. Division II will be significantly less intense than manual I, and division III still less than II (compare this to a Cavaillé-Coll, where division III (récit) is usually quite strong, and crescendo is obtained via the swell box precisely thanks to this strength).
In particular, replacing pallets by cones is not a goal in it self, but merely a technical necessity resulting from the different kind of grooves.
These cones do, however, have an influence on the attack of the sound (and on the touch, if it's a tracker action, since there will be much less pluck). Afficionados usually consider this influence to be positive on overblowing stops, strings, and free reeds, which are precisely very typical for this kind of instruments.
If you can get hold of Ludger Lohmann's CD at Schramberg (Ritter's four sonatas) or of Gerd Zacher's CD at Essen-Werden (Reger opp.73 and 127), you'll get a pretty good idea of what I'm saying.
Needless to say, don't try to play Bach on these instruments!