This paper evaluates the role and effectiveness of different types of haptic feedback in presenting relevant feedback information during needle insertion in soft tissues through a remotely operated robot. We carried out three experiments with human subjects to analyze the effect of grounded kinesthetic feedback, cutaneous vibrotactile feedback, and cutaneous pressure feedback for rendering the elastic and the viscous force components of a simplified needle-tissue interaction model in a simulated environment. Results showed that providing the two pieces of feedback information through different channels, i.e., kinesthetic and cutaneous, led to the best performance, yielding an improvement in detecting a different tissue layer with respect to providing both information through the same commercial grounded kinesthetic interface. Moreover, results indicate that cutaneous pressure feedback is more suited for rendering the elastic component of the interaction with respect to vibrotactile cutaneous sensations. Finally, results suggest that rendering this elastic component where the user holds the input interface is not so important, confirming that delocalized cutaneous sensations can be an effective solution.