“Inviter à” is more common but it depends on the situation. Sometime it will make more sense to say à, au or dans.

You wouldn’t use commonly these two sentences. What is currently used is the idiomatic expression “inviter au restaurant” and that means about any restaurant most of the time. If you want to express in French the idea contained in either of those two sentences you’d habitually use a longer form.

• Nous vous inviterons à un repas/diner dans un grand restaurant.

The meal takes place in the restaurant. It’s an invitation to a meal/to share a meal basically. “À” can’t be used in place of “dans” here.)

However, it seems that nowadays people use a lot “inviter dans un restaurant” but not “inviter à un restaurant“.

Inviter à is the usual phrasing when it is followed by a verb.

• Il m’a invité à manger au restaurant.

When inviter à is followed by a noun (or a noun phrase) which preposition you use will depend on what this noun represents and how you relate to it.

• Je suis invité à son anniversaire.
  → an event
• Nos voisins nous ont invités chez eux.
  → a place that is usually preceded by chez
• Ils nous ont invités dans leur maison de campagne.
  → a place you can walk into/as opposed to another place (e.g. chez eux)
• Ils nous ont invités sous leur tente.
  → a place you usually stay under

In the specific case of your question we have to consider un restaurant vs un grand restaurant.

• Nous vous inviterons au restaurant.
  We are referring to the act of eating out without specifying a particular place. We have no particular restaurant in mind when we say those words (in spite of the fact that au stands for à le), we would not use dans in that case.

• Nous vous inviterons dans un grand restaurant.
  Although we are, of course, still talking about eating out, we are here referring to a particular kind of restaurant: un grand restaurant. We are talking about a particular place where we can sit in, walk in or out. And that’s why in this case we would use inviter dans un grand restaurant.