Normally plants which have a taproots have a bigger size plant size such as almost all the tree plants as well as vegetable crops, that means those plants require more water and nutrients, so taproots suppose to be more active to absorb both water and nutrients.
In active roots, there is a zone with root hairs. This zone is actively absorbing water and mineral ions. The root system has the other important function of anchoring the plant to the soil. So, the other parts of the roots are only facilitating the movement of water and ions to the leaves but they have a minimal role in water and ion absorption.
all roots are certainly perfectly capable of performing both tasks but various plant species, especially in dry climates, have a specialised dimorphic root system consisting of a deep-reaching taproot to access deep soil water resources and groundwater and a more or less dense network of horizontal lateral roots in the topsoil primarily responsible for nutrient absorption (together with mycorrhizae if present). In some cases, lateral roots may also develop so-called sinker roots growing vertically down in support of the taproot (i.e. to promote water uptake). Hope that helps!
1. Most dicots have a taproot system, while most monocots have a fibrous root system.
2. Some plant taproots have specialized into a storage organ such as carrots and sugar beets to store food like carbohydrate, some taproots have modified into reaching deep water in the ground. So, it is hard to compare which one absorbs more water, taproot or fibrous root system.
3. Actually, most water and nutrients are absorbed by 'roots hairs',a hair-forming cell on the epidermis of a plant root. They are found only in the region of maturation of the root, and the structures allow a plant to get water and nutrients from the soil.
4. We may not know precisely which root system absorbs more water/nutrients among different species, but we do know that plants know exactly how much water/nutrients they need to grow and finish a life cycle to have progeny. An environment with too much or too less water/nutrients, they will suffer, stressed and die.