I got offers from Birmingham, Warwick and Coventry - I chose Coventry. I found there is much greater sense of purpose at Coventry, and did not personally connect with the other universities. Coventry is majorly concerned with sustainability, the environment and engineering advances and that stood out to me when making my decision. I don't want to go to a university where I'm simply learning formula and writing it down in tests. Coventry gives you a holistic experience to set you up for life. Through their system I have managed to become a Campaign Leader, Halls Rep, Student Councillor for my course, am now opening my own business thanks to the Entrepeneurship scheme that Coventry has (due to Sir John Egan's funding) and have landed a job placement starting in January to work inside the Student Union for the university itself. University isn't all about the degree, it's about growing up academically and as a person.
As for the actual question about being close to Warwick - Coventry is nowhere near Warwick on foot so I have never come across the other university. Even if Warwick was next door, it really doesn't matter. We're here to better ourselves and we're not against one another. Warwick university generally don't intend on intimidating other universities - that's just silly.