Botanical Garden or Arboretum and Nature Center? or both?

Hi – I am planning a trip to Houston in mid April and I am trying to decide if we should go to the arboretum and nature center or the botanical garden? or both We are planning on visiting the museum of natural history, but are unsure if we should do the garden or the nature center or if it is worth it do to both.

Also looking for good food and drink places – hole in the wall type places would be great! We love all genres to food, only issue being shellfish and banana allergies.