When she goes to Mexico, she will be visiting Chichen Itza.
When she goes to Mexico, she will visit Chichen Itza.
Is there a particular difference in meaning, or it is just the matter of style?
As other answers have indicated, the future progressive, as the term implies, can place emphasis on the ongoing nature of the future event. In such contexts the future simple is not correct:
This time tomorrow I’ll be lying (*I’ll lie) on the beach.
Sorry, I won’t be able to make it. I’ll be playing (*I’ll play) tennis
However, this is not the only use of the future progressive. It is often used when there is no particular focus on the ongoing nature of the future event:
You’ll be hearing from my lawyer.
She’ll be starting school soon, won’t she?
In such cases, the future simple is also possible:
You’ll hear from my lawyer.
She’ll start school soon, won’t she?
although, to my ears at least, these are very slightly less natural.
Now we come to the OP’s examples, both of which are perfectly normal ways to tell someone of your friend’s holiday plans.
There is possibly one small semantic difference, however. Namely, that the progressive form could carry with it the implication that the visit is part of an arrangement, whereas the future simple is a simple statement of fact. As such the future progressive parallels the use of the present progressive to express arranged future events:
I’m playing tennis with Mike tomorrow.
I’m visiting my grandparents at the weekend.
She’s visiting Chichen Itza next week.
But in Fumblefinger’s term, this is “armchair rationalisation“, a process that no native speaker consciously goes through in advance of what they say in day-to-day conversation.
In summary, the OP’s two sentences are virtually equivalent, but there are other contexts where only the future continuous is possible, or where it may sound a little more natural than the future simple.