If you let her tile the apartment, but not the kitchen, then make sure enough extra tiles are ordered for the kitchen. You don't want to risk that the same tiles are not available after a number of years.
You should make sure the tiles of her choice also increase the value of the property. If she objects with the argument she pays for them, then you should offer to pay a part of it.
Tiles, if they do not break, require less maintenance than carpet. Carpet gets dirty and needs to be replaced after a number of years. Tiles just need a wash. Make sure the tiles are suitable for floor. And double check that the floor is stable enough for tile, so that they won't break.
Think about what is under the apartment. Is it a cold floor? Tiles are much colder to the feet than carpet. In Norway we install warmth cables or water heating pipes under a tile floor to make it warm in the winter. If someone else lives underneath, a tile floor can give more noise to the person under (high heels on tiles). Under a wooden floor you can put foam material, but I don't know if something similar can be done with tile.