When deciding whether to use rocks instead of mulch, you should first understand what the purpose of mulch is in your garden and then decide whether you can forego using mulch in favor of rocks.
Mulch is made from organic matter such as wood chips, sawdust, pieces or shavings. Because the mulch is organic matter, it decomposes over time and will need to be replaced every year or so. While this is an expense, it ensures that your soil is regularly fed with nutrients from the mulch.
Mulch is light and can easily be blown around, not very helpful if you have a windy climate. On the flipside, because the mulch is lightweight and decomposes, it is good for flowerbeds that require regular maintenance to replace bedding plants and the like. The mulch is also easy to work with when removing weeds.
Some people prefer rocks instead of mulch because, although initially expensive to add, they do not need replacing. The look of rocks is attractive and contemporary and can lighten the garden if you choose light color rocks.
Rocks obviously don’t blow away because of their weight. However the weight means that rocks are not a good choice for beds that need attention, as they need moving. Although rocks are permanent, they add nothing to the soil which means you have to be careful about what you plant. Certain plants need a lot of nutrients and all soil will eventually need some kind of organic matter such as compost to enrich it and ensure your plants thrive.
Rocks instead of mulch are not a good alternative in all parts of the garden. Rocks work well with alpine plants that are naturally used to rocky areas. Rocks can also be added to areas where there are small trees and other more established plants that need no seasonal attention, but eventually they still might need some compost.
If you love the look of stone, then consider adding potted plants to your garden that you then cover with large stones. Or use gravel as an alternative to grass so that you get the look without changing your flowerbeds.