When to use functional setState

First things first, in your case the two syntaxes are entirely different, what you might be looking for is the difference between

this.setState({pictures: this.state.picture.concat(pics)})

and

this.setState(prevState => ({
   pictures: prevState.pictures.concat(pics)
}))

To understand why the second method is a preferred one,you need to understand what React does with setState() internally.

React will first merge the object you passed to setState() into the current state. Then it will start that reconciliation thing. Because of the calling setState() might not immediately update your state.

React may batch multiple setState() calls into a single update for better performance.

Consider the simple case, to understand this, in your function you might call setState() more than once like:

myFunction = () => {

   ...
   this.setState({pictures: this.state.picture.concat(pics1)})
   this.setState({pictures: this.state.picture.concat(pics1)})
   this.setState({pictures: this.state.picture.concat(pics1)})

   ...
}

which isn't a valid use case in a simple app but as the app gets complex, multiple setState() calls may be happening from multiple places, doing the same thing.

So now to perform an efficient update, React does the batching thing by extracting all the objects passed to each setState() call, merges them together to form a single object, then uses that single object to do setState(). According to the setState() documentation:

This form of setState() is also asynchronous, and multiple calls during the same cycle may be batched together. For example, if you attempt to increment an item quantity more than once in the same cycle, that will result in the equivalent of:

Object.assign(
  previousState,
  {quantity: state.quantity + 1},
  {quantity: state.quantity + 1},
  ...
)

Subsequent calls will override values from previous calls in the same cycle, so the quantity will only be incremented once. If the next state depends on the current state, we recommend using the updater function form, instead:

this.setState((state) => {
  return {quantity: state.quantity + 1};
});

For more detail, see:

• State and Lifecycle guide
• In depth: When and why are setState() calls batched?
• In depth: Why isn’t this.state updated immediately?

— setState() - Other APIs - React.Component – React.

So if any of the objects contains the same key, the value of the key of the last object with same key is stored. And hence the update only happens once with the last value.

Demo Codesandbox

TL;DR: Functional setState is mainly helpful to expect correct state update when multiple setStates are triggered in a short interval of time where as conventional setState does reconciliation and could lead to unexpected state.

Please check this wonderful article on Functional setState to get a clear understanding

And here is the WORKING DEMO

Firstly, you are trying to do different things in each of your cases, you are assigning pics in one and concatenating pics in another.

Lets say this.state.pictures contain [1, 2, 3] and pics contain [4, 5, 6]

this.setState({pictures: pics})

In the above case this.state.pictures will contain the pics i.e this.state.pictures = [4, 5, 6]

this.setState(prevState => ({
   pictures: prevState.pictures.concat(pics)
}))

Whereas in the above snippet, this.state.pictures will contain the previous pictures + pics i.e this.state.pictures = [1, 2, 3, 4, 5, 6]

Either way you can tweak it to meet your API needs, if it's like a paginated response the you are better off concatenating the results on each request, else if you get the whole array each time just assign the whole array.

Conventional setState VS Functional setState

Now, your question mainly is probably whether to use setState with an object or with a function.

People use both of them for different reasons, now the functional setState is said to be safe because React does something called a reconciliation process where in it merges multiple objects inside setState when triggered frequently or concurrently and applies the changes in one shot, kind of like a batch process. This could potentially lead to some unexpected results in scenarios like below.

EXAMPLE:

increaseScoreBy3 () {
 this.setState({score : this.state.score + 1});
 this.setState({score : this.state.score + 1});
 this.setState({score : this.state.score + 1});
}

As you would expect the score to be incremented by 3 but what React does is merge all the objects and update the score only once i.e incrementing it by 1

This is one of the cases where functional callback shines because reconciliation does not happen on functions and executing the below code will do things as expected i.e update score by 3

increaseScoreBy3 () {
 this.setState(prevState => ({ score: prevState.score + 1 }));
 this.setState(prevState => ({ score: prevState.score + 1 }));
 this.setState(prevState => ({ score: prevState.score + 1 }));
}