I've come across some c code for a PIC timer where we can either load a value directly into the timer, define a 16-bit variable and split its high and low bytes into their respective registers (TMRH and TMRL), or define another uint16_t variable like this:

load a value directly into the timer

uint16_t TMR = 1110;     // Define a 16-bit variable with an initial value of 1110

Split its high and low bytes into their respective registers (TMRH and TMRL),

uint16_t values = 1110;  // Define another 16-bit variable with an initial value of 1110

// Split the high and low bytes into their respective registers
TMRH = (values >> 8) & 0xFF; // Load the high byte of 'values' with 4
TMRL = values & 0xFF;        // Load the low byte of 'values' with 74

Could you explain the benefits of each approach and when it's preferable to use one over the other?

 

You have defined TMR as 16 bits. The compiler will do the work for you but it still has to read/write two bytes.
On some MCUs, the order by which you read/write the bytes is important. Check the MCU User Manual.