The cards are considerably more complicated electronically. Additional power would be needed to drive the ARM processor vs. a typical SD controller. Once you add in Wi-Fi radio and the encryption requirements that come with it you should expect an impact on battery life (though most cards now shut down Wi-Fi when it is not transmitting which helps.) The cost of a spare battery vs the ability to have access to Terabyte scale storage and immediate availability on screen for editing / post seems like reasonable tradeoff if you will use those features.
Another effect will be on performance. Eye-Fi, who licence their technology to others including Transcend and Sandisk, has a product line made of mainly SDHC class 4 with some 6's and a couple of 10's. At this point (July 2014) none of the major players (Eye-Fi, Transcend or Sandisk**) offer any UHS-1 and UHS-3 devices which would suggest that the processor imposes performance limitations beyond the flash memory. If you're shoot a lot of bursts or action then this may affect your decision.
Beyond those your consider are just like adding any other gadget to your ecosystem. Will it physically connect? Is the software compatible with everything else? Does it have dependencies (on software for example?) How will it affect your workflow?
** I've not forgotten Lexar, they have no Wi-Fi cards in their product line up. They had one in 2008 under the name Shoot-n-Sync.