I'm going to shoot a lot of Electronic News Gathering stuff like demonstrations, reports. But also interviews and longer events like speeches and talks. I can't decide between a camcorder and a MILC (mirrorless interchangeable lens camera) because both have their pros and cons. I like in the MILC that it has a lot of possibilities to develop later. I have a candidate for both categories. The JVC Everio GC-PX100 as a general camcorder and the Sony Alpha 7 as a MILC. I like about the Sony that it's a full-frame, very serious camera. But I'm afraid that it lacks some important features or not very good at some fields, like OIS or autofocus. I never worked with a DSLR or MILC before. The JVC would be a safe bet but also a great loss in features due to the fixed lens and small sensor.
If you record speeches that are longer than 30 minutes, the 29m59s limitation of non-video cameras is going to drive you crazy, despite all the other wonderful things they can do. Interviews can be broken up every 30 minutes. Speeches not.
If you have ambitions to encompass art projects with your camera, the interchangeable lens feature of the SONY camera opens a world of possibilities (and and bottomless pit of budget requirements). If you are really focused on ENG then the JVC packs an incredible punch in a single package. Plus, small sensors are your friend for ENG because of deep depth of field. It's incredibly annoying to have a speaker in front of a screen and the camera can only focus either on the speaker or their slides.
Based on the things you say you want to do, not the things you say you want, the JVC is the more sensible choice.
Another point that Michael didn't mention is ergonomics. Using a MILC camera means that you will need an external monitor (the viewfinders are never good enough to judge critical focus, and with the short DOF you need to be on top of that), which means some sort of rig to hold it, maybe an external battery, external sound recorder, shoulder mount… so you end up with something that looks like it was built out of meccano. Fine for a studio or film set, atrocious for documentary work.
Mind you, I'm not liking the shape of that JVC camera in this regard. Looks too much like an SLR for my money. Where's the eyepiece?
If you hope to record ENG footage for TV submission, make sure that the camera can record in a format that is permitted by the stations you hope to be working for. In the case of the station I work for, news footage can only be submitted as interlaced (1080i50) and a lot of photocameras with video function can not shoot interlace video.