Full disclosure: I work for Bitcentral
Four years ago, I was where you are now. I was a chief editor and photographer for a station in New Orleans. We were not using Avid but rather DVC Pro. We were a team consisted of mostly 15 to 20 year veterans that were reluctant to make any changes. We were faced with having to use Adobe Premiere Pro and Bitcentral as our play out.
As far as Bitcentral goes, the play out changes will be no problem for photogs and editors. Pushing to air is simple, the interface is easy to use, and archiving is automatic. Many of the interfaces use Firefox. Pretty much, if you can use Google, you can use them. Your biggest change will be in the editing suite.
After training several stations that use Avid, I think I've pretty much figured out the biggest fear that they have. What is it you may ask? Adobe Premiere is not Avid. Most users get so used to using a single interface, that they won't open their mind to using something new. They're different, but that is in exactly a bad thing. By the end of the training, most users have told me that they can see the benefits of the switch.
When we first got Adobe Premiere at my station, version CS5 wasn't exactly ready for prime time news editing. But over the last several years new versions of the software, subsequently have each added several new features that make things more convenient than the previous version. The newest version of Adobe Premiere CC 2014 has added a really neat masking and tracking effects.
The biggest change that you will see between the two is organization. Since Avid was an all in one unit, things were slightly more integrated. Premiere doesn't really care how you have things organized. Like Land Rover mentioned, things can get messy. You can be as messy or as neat as you want in your organization. Premiere will find the files as long as you don't rename them or move them from their original file location. This can be good and bad at the same time.
But just like the old days of tape or film, you need to be deliberate in where your raw materials are going. Bitcentral will work with the station to set up an organization workflow so files won't be so random and messy.
I'd have to agree with many of the things that MidwestPhotog said. The thumbnails are quite nice. As far as the crashing goes, I find that it really can vary depending on your hardware, RAM, etc. The system runs on a PC, so crashes can happen, but I find that proper file maintenance and a regular reboot schedule seems to improve on this.
You can always try out for Premiere before the station goes live though. Adobe gives 30 day free trials on their website for all of their programs. I'd encourage you to try it ahead of time so you can get a feel for the interface. If you have any questions on a particular topic or how things work, you can always send me an email.
Chances are, I will be one of the project managers that will be sent out to your station for training. So if there's anything I can do to help, please don't hesitate to contact me.