With conditionals (IF ... THEN), like your first example, the 'rule' (it's far more complicated, really, because some specific situations call for different constructions) is that the tense-bearing verb in the condition (IF) clause and WILL in the consequence (THEN) clause take the same past/non-past tense:
If the price goes [non-past] up I will [non-past] buy it.
If the price went [past] up I would [past] buy it.
If the price had [past] gone [perfect] up I would [past] have bought [perfect] it.
It is the function (IF or THEN) of the clause, not its position in the sentence, which governs:
I will [non-past] buy it if the price goes [non-past] up.
I would [past] buy it if the price went [past] up.
I would [past] have bought [perfect] it if the price had [past] gone [perfect] up.
Note that will here does not express tense; it implies consequence, not futurity. You may substitute may/might or can/could for will/would in all these examples.
The situtation is different in your 'shopping' example, where will/would in the subordinate clauses does express tense, and must be deployed accordingly. Let's look at two different situations:
She told me last week that she would go grocery shopping yesterday, but I told her her I would not be able to go with her.
In this case the shopping trip was in the future when you spoke with her but is no longer in the future; you must employ the past form of will.
She told me last week that she will go grocery shopping tomorrow, but I told her I will not be able to go with her.
She told me last week that she will go grocery shopping tomorrow, but I told her I would not be able to go with her.
In this case the shopping trip is still in the future; you were unable to accompany her then and you still are unable to accompany her. You may use either will or would, depending on which timeframe you want to communicate.
Those are three different tenses.
walks (third person singular present tense; regular action or habit)
— She walks everyday.
walked (past tense; completed action on a specific time)
— She walked yesterday.
will walk (future tense; planned stuff to do in the future)
— She will walk within two days.
Best Answer
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:
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:
In such cases, the future simple is also possible:
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:
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.