Need Advice - job offer

I verbally accepted a job offer that won't start until beginning of June. In the meantime (as in Thursday), I was offered a job that pay 17k more per year and is more flexible. It was a job I applied for over a month ago and actually did not think I was in the running for - it took a long time for them to complete the interview process because the hiring person went out on emergency FMLA.

I am having a hard time trying to figure out how I am going to tell the very nice people who offered me the first job and I accepted. I feel like I will be going back on my word - suggestions on how to let them know I have changed my mind. Another thing is I kind of convinced this dept to hire me because I didn't really have the qualifications they were looking for and I think that is why I feel so bad about this.
It says a lot about your integrity that this bothers you, but in the end, you have to do what is best for you. I have been a nurse almost 40 years and while I am always loyal to my employer, I realized early on that my hospital was there when I was born, and it will be there when I die. What I do in the mean time, is up to me.If you decided to take the second job (and the sooner you decide, the better), send a politely written letter to the one you verbally accepted, telling them, "after careful consideration, I are unable to accept your offer of employment. Thank you for offering me this opportunity, blah, blah, blah". Be concise and professional and never burn a bridge.Good luck