I'd say that weather in both is about the same, but Raleigh is a bit cooler in the summers. It is also closer to the coast so you tend to get affected by tropical storms and hurricanes more than the Charlotte area does. It's rarely bad here, but once every ten years or so there is some flooding from a hurricane.
As for jobs, both cities are the best places in the state for employment. Raleigh/Durham has RTP which is well known as the home of many tech companies, so if you are in a tech field it is a great place to look for a job. There are also a number of hospitals in the area, including the Duke and UNC hospital systems which are huge. Raleigh also has a couple big WakeMed facilities and Rex, so nursing jobs are fairly abundant here.
I've lived near Charlotte for a short time and currently live in Cary, near Raleigh. I think they are similar cities. The big difference is that Charlotte is bigger and a little more metropolitan. The downtown area there is well established and there are a number of things to do. By comparison, Raleigh's downtown is mainly government related with a few pockets of urban downtown living. Areas in Durham's downtown have really come along in recent years making it a desirable place to live and visit. Still overall Charlotte has more of a big city feel that the Raleigh Durham area.
It's really a matter of opinion as to which is better. Having lived in both, I would not want to live in Charlotte. Just a personal opinion. Housing in both is equally affordable if you are coming from anywhere in FL that's been part of the housing boom there. You could probably get a starter home in or near both cities with a decent sized lot for ~$150k. Obviously you can spend as much as you want as there are very affluent neighborhoods in both areas as well.
Good luck and if you have more specific questions please post them.
To the above post - we have the Hurricanes (Stanley Cup champs!) and all of good NC ACC teams within 30 minutes of each other. The Bobcats...who are they??