I think that the question is too vague and has too many variables for any determination to be made. It seems to me to be a matter of weighing several facts which We don't have.
You want someone qualified and 'up' on the technology to install your Lan and Communications wiring. Is the Electrical Contractor as qualified in this aspect as a specialist would be? He may very well be, and that would be the best scenario. But if he's not, there's nothing wrong with having 2 'specialists' work on your project. As to pricing ?? Ask for estimates.