Simply my own experience, but here's the rundown:
Republic had been recruiting at my university for a while and signed some agreement, and now they come about 3 times a year. Announced they would be doing cadet interviews for any student with at least an IR. I was starting my commercial so I polished my resume and tried to read through gouges/forums and studied up. On that day in particular, only HR was there, no pilot. She gave me an iPad while looking over my resume and current transcripts (still had a few semesters left of school), where I took a short written. I hadn't taken an ATP written before, but they were neither the questions you'd see on ATP level writtens nor were they super basic. It's been a while so I don't remember the exact questions, but I want to say they were things like airspace, weather, IFR mins, etc. I think it just gave me 20 random questions from a bank, and I didn't see the results. She then conducted an oral HR evaluation, consisting of a mix of "tell me about you" questions as well as "tell me about a time..." Since there was no hiring pilot there that day, she had to do his side of the interview as well. She's not a pilot, but I guess had been doing interviews for enough years to know the general gist of the answers they look for, but just like with the written I got no real feedback or gauge of how well I did. Then she gave me some Republic info (E170 cockpit poster, cadet program overview, etc). I got an acceptance email the next day.
All in all, it was about 10% of the intensity I expected (i.e. I was expecting something closer to all the typical airline interviews I hear about). I don't know if it was watered down because they have some agreement with our part 141 school, so take it with a grain of salt. I even shaved and showed up in a suit, whereas most of the other people I saw interview that day were just wearing whatever. I basically got the feeling that, as long as my grades were good and I hadn't failed every checkride, I would have gotten the offer unless I just bombed the interview.
The cadet program has been neat. I'm done with school now but when I was still there, they'd take us out to dinner when the recruiters were in town. It offered an opportunity to meet with them more personally (i.e. not on company time and in uniform, so they tended to be more frank in discussion). I even was able to make it to a cadet event back in May. Bought me a ticket to IND, put us up in a hotel, took us to their HQ and played around with their GFS sims, and then we got to go to their suite at the speedway and see a practice day for Indy 500.
I won't lie, initially I was just keeping the offer as a fallback, and to take advantage of the perks they were offering. She mentioned in the interview that anyone who makes it into the cadet program doesn't have to interview again (i.e. do the "real" interview), so it was a nice ace in the hole. No commitment like some of the other regionals sucker you into (as has been mentioned). Now, I'm looking more critically. There are really only two or three regionals I'm looking at and Republic is definitely one of them. They offer a pretty nice signing bonus, there's the Flight Time Initiative if you need that, and then all the other plusses (own their planes, common fleet type, proven record, big and reliable company, etc). As I accrue my hours over the next year, I'm just keeping a close eye on everything, but based on the status of the industry right now, it's either SkyWest if my wife and I want to stay out west, or Republic if we move east.