Header navigation with React
Quick review.
This is a very basic review as I am not a react fan. Do not accept this post as an answer or you will likely dissuade others from adding a better one.
Your question

&quot;I used a switch statement in getContent to avoid having an array of objects in memory all the time. Is it actually better performance-wise ?&quot;

By &quot;better performance-wise&quot;  I assume you mean CPU cycles. The answer is, &quot;No its not better.&quot;
Computation complexity
For 2 items the difference is tiny, but if you had a long list of items say n is number of items. To display the last item would require n comparisons so worst case is O(n), and best case display the first item is O(1). Picking random items the complexity is O((log n)c) with c just above 2 (AKA polylogarithmic)
What you had return this.state.content[this.state.cidx];, basicly a lookup table, is O(1) the best performance you can get.
Storage complexity
Many times there is a price to pay for using a lookup table and that is memory. But in this case that makes no difference as you are after already stored items rather than looking up a precomputed value.
As I understand it the react elements you defined as &lt;Heroes/&gt;, &lt;Teams/&gt; are store in an internal node tree, having them in an array means you have an extra item in the state object to reference the array and one reference per item. That would require storage O(2n + 1) rather than O(n). Where n in this case refers to a reference to the react elements, not the elements themselves.
O(2n+1) and O(n) are the same, and tiny compared to the elements actual needs.
Style
You could make a slight change
  updateContent(idx) {
    this.setState({cidx:idx});
  }

to
  updateContent(cidx) {
    this.setState({cidx});
  }

But really I only say so as filler as your code looks good, like its almost a cut and paste from the best of react, a good thing (I am not implying you cut and pasted anything )
I do have a long list of style points in regard to your code, but as that list directly contradicts the react style guide it would be rather bad advice.
Merry Xmas