No, if you want to register a trademark, the price doesn't depend on whether you apply for a word mark or a figurative (logo) trademark (or any type of trademark, for that matter). The cost will be primarily influenced by your choice of country, the number of trademark classes you apply in, and maybe your legal representative's fee.
The type of trademark impacts how its protection should be understood, compared to others and applied. When thinking about concepts of distinctiveness and similarity, two essential criteria for trademark registration, there's a difference between how these apply to a word/phrase and a visual representation (even if it was a visual rendering of the same word/phrase). Brand names, logos, sounds or smells cannot be easily compared to each other, hence why the system exists.