In general the plants are ok with either. I suggest steering clear of very dark stone though as it gets hot in the sun and can burn plant foliage. White stone does not get hot but it is impossible to keep white.
Crushed stone is often the most cost-effective option while smooth and rounded gravel has a more natural look like the beach or a river bottom. Fabric should be used under stone. It will not permanently eliminate weeds but it does keep the stone from sinking into the soil.
Cedar mulch has long been popular due to the misconception that it keeps bugs away. Termites and carpenter ants eat wood but have no interest in bark. Cedar loses its color quickly and meshes so tightly that it keeps water away from the plants.
You will be better off with pine, spruce or hemlock. The dyed mulches hold their color well but they are usually wood instead of bark which means they blow around when they dry out and have less insulating benefit for the garden.