Merino wool holds its own across a wide range of temperatures and resists picking up odour far better than synthetic fabric, since the fibre structure itself limits the bacteria that cause smell. That makes it a strong choice for multi-day trips where washing isn't an option, or for lower-output days where you're not sweating heavily.
Synthetic base layers, usually polyester or a polyester blend, dry faster than merino and wick sweat quickly during hard, sweaty effort. They also tend to cost less. For running, fast hiking or any activity where you're working hard and need the fabric to keep up, synthetic is the more practical pick.
Some base layers blend the two, aiming for merino's odour resistance alongside synthetic's faster drying time, at a cost partway between the two fabrics.