The issue would seem to be one of muktza - objects that may not be moved during shabas because they are not for shabas use. Let us assume that a standard watch is not muktza because it is a k'li shem'lachto l'heter - its normal usage is permitted on shabas. (See the last line of the long paragraph on this convenient Google hit.)
The complex devices to which you refer have this functionality as well as some other functionality. If the additional functionality were to prohibit the otherwise permissible watch, it must be because we assess those functions separately, as if it were a hybrid between a watch and [for example] a remote control. The latter would be a k'li shem'lachto l'isur - a tool whose normal usage is prohibited on shabas, which is consequently immovable barring special circumstances. If so, we have a case of one muktza object inextricably attached to one non-muktza object, which is addressed by Ramba"m in his Hilchos Shabas 25:14,15. He says that moving the assemblage for the permissible item is permitted while moving it for the prohibited item is prohibited.
The above makes the assumption that anything strapped to the wrist that has a clock face is defined as a watch regardless of its other accessories.
(The other exceptional case you mentioned - an especially elegant watch that is considered jewelry - might actually present an unrelated muktza problem, which is concern for chisaron kis - monetary loss. Very expensive objects are muktzim as well.)