With phenotypic screening, if you find a hit, you know that it is capable of getting into the cells, but you can't be sure it is hitting the intended target. You may not even have any idea of what the target is in a simple screen for inhibition of cell multiplication. You then have a potentially difficult job of identifying the target.
With target-based screening, if you find a hit, you know that it is inhibiting the target, but it may not be able to get into the cell. Also, the conditions of the screen may be so different from the intracellular conditions that inhibition in the screen does not translate into inhibition in the cell.
With phenotypic screening, you have no control over the intracellular conditions and therefore no ability to tune the sensitivity of the assay to inhibitors (the exception is when the target expression is reduced to enhance the sensitivity of the cells to loss of activity of the target).
In either type of screen, the quality of the compounds is of great concern. Some compound libraries are full of compounds that no medicinal chemist would find interesting. Many are well-known non-specific inhibitors. Often, the compounds are in poor condition or impure. Obtaining clean, fresh samples of actives that look interesting is a valuable first step in hit follow-up. Do not rely on the DMSO stock solutions from the screening deck.
My experience with screening was that most actives from a screen were false positives or had undesirable modes of inhibition. It is very important to have the tools to find the interesting compounds quickly amidst all the uninteresting ones. My opinion is that having the biochemical and biophysical tools available with some purified protein targets is highly advantageous for building a hit evaluation test cascade.