Lookup table vs switch in C embedded software

In another thread, I was told that a switch may be better than a lookup table in terms of speed and compactness.

So I'd like to understand the differences between this:

Lookup table

static void func1(){}
static void func2(){}

typedef enum
{
    FUNC1,
    FUNC2,
    FUNC_COUNT
} state_e;

typedef void (*func_t)(void);

const func_t lookUpTable[FUNC_COUNT] =
{
    [FUNC1] = &func1,
    [FUNC2] = &func2
};

void fsm(state_e state)
{
    if (state < FUNC_COUNT) 
        lookUpTable[state]();
    else
        ;// Error handling
}

and this:

Switch

static void func1(){}
static void func2(){}

void fsm(int state)
{
    switch(state)
    {
        case FUNC1: func1(); break;
        case FUNC2: func2(); break;
        default:    ;// Error handling
    }
}

I thought that a lookup table was faster since compilers try to transform switch statements into jump tables when possible. Since this may be wrong, I'd like to know why!

Thanks for your help!