Should users say thanks either in the comments or in the question itself?
I agree with @Pawel, though if you are responding anyway it doesnt hurt to throw in another word of appreciation.
Also, if someone took the time to write a long, comprehensive, or thoughtful answer, I think you could show your appreciation by discussing the content. Or, upvoting always works too :)
@Bubby4j - Thanks for the question. I'm sure users new to the SE environment will be interested in this issue.
Appreciation is always nice to receive, as well as polite and friendly to give. However, as this is a Q&A site with other means in place of showing (albeit anonymously) your gratitude, it is not something that should solely comprise the content of a post - whether it be a question, answer, or comment.
While comments may not greatly affect the loading weight of a page, they do have a measurable impact on the vertical real estate that is taken up by the question or answer post to which they are attached. Over-commenting, even by only one or two, can quickly make a question or answer look very bloated and the entire thread just becomes cumbersome and unpleasant to scroll through.
If you're making a post that actually furthers the discussion in some way, by all means do include an expression of your thanks in that post as long as you have enough characters left in your limit (if applicable) to do so.
Otherwise, please don't make a post for the sole purpose of saying "thanks". That's what up-votes and answer acceptance are for. People do notice the bumps in their rep, and the numbers next to their posts, so your appreciation (while it may not be attributed) will assuredly not go unnoticed.