The online hate speech is proliferating with several organization and countries implementing laws to ban such harmful speech. While these restrictions might reduce the amount of such hateful content, it does so by restricting freedom of speech. Thus, an promising alternative supported by several organizations is to counter such hate speech with more speech. In this paper, We analyze hate speech and the corresponding counters (aka counterspeech) on Twitter. We perform several lexical, linguistic and psycholinguistic analysis on these user accounts and obverse that counter speakers employ several strategies depending on the target community. The hateful accounts express more negative sentiments and are more profane. We also find that the hate tweets by verified accounts have much more virality as compared to a tweet by a non-verified account. While the hate users seem to use words more about envy, hate, negative emotion, swearing terms, ugliness, the counter users use more words related to government, law, leader. We also build a supervised model for classifying the hateful and counterspeech accounts on Twitter and obtain an F-score of 0.77. We also make our dataset public to help advance the research on hate speech.