Does common beach sand contain more or less silica than an equal amount of powdered Basalt?

White beach sand is often largely quartz, which is pure, crystalline silica i.e. silicon dioxide. Basalt includes additional elements like iron, sodium, potassium, manganese, etc. which means there is less silicon than in quartz. However, your answer will depend on the sand, because beach sand can be composed of any combination of minerals that are around the area. Black sand beaches are usually composed of basalt.

From the Wikipedia entry "Sand":
The composition of sand varies, depending on the local rock sources and conditions, but the most common constituent of sand in inland continental settings and non-tropical coastal settings is silica (silicon dioxide, or SiO2), usually in the form of quartz. The second most common type of sand is calcium carbonate, for example aragonite, which has mostly been created, over the past half billion years, by various forms of life, like coral and shellfish. For example it is the primary form of sand apparent in areas where reefs have dominated the ecosystem for millions of years like the Caribbean.

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The composition of mineral sand is highly variable, depending on the local rock sources and conditions. The bright white sands found in tropical and subtropical coastal settings are eroded limestone and may contain coral and shell fragments in addition to other organic or organically derived fragmental material, suggesting sand formation depends on living organisms, too.[3] The gypsum sand dunes of the White Sands National Monument in New Mexico are famous for their bright, white color. Arkose is a sand or sandstone with considerable feldspar content, derived from weathering and erosion of a (usually nearby) granitic rock outcrop. Some sands contain magnetite, chlorite, glauconite or gypsum. Sands rich in magnetite are dark to black in color, as are sands derived from volcanic basalts and obsidian. Chlorite-glauconite bearing sands are typically green in color, as are sands derived from basaltic (lava) with a high olivine content. Many sands, especially those found extensively in Southern Europe, have iron impurities within the quartz crystals of the sand, giving a deep yellow color. Sand deposits in some areas contain garnets and other resistant minerals, including some small gemstones.