I guess that depends on how you define "criminal." While I arrested my share of thieves, burglars, DWIs, drug users, and drug traffickers, I never arrested anyone for what is known as "crimes against persons." The other crimes impact people, but, not to the same extent. So, honestly, while it felt good to catch them, it was not some big feeling of accomplishment, it was just doing my job.
When you arrest a criminal, they are rarely put away "for good." First there is bond, which lets them get out prior to trial. Then there is the chance of probation. Then, even if sent away, they can get parole. And, there are always appeals.
Incarceration is a huge industry, employing many people. However, we lock up more people than any other nation. There are better ways to deal with some of the less serious crimes. When you lock someone up, they are exposed to more hardened criminals, and they can easily get worse rather than reforming.
You also need to consider the person's family. The idea that children are growing up without parents because the parents are locked away, further contributes to the decline of society. Actions I took stopped a mother from attending her daughter's wedding, and a son from attending his mom's funeral. While this was ultimately their fault, it still causes you to stop and think about what you are doing.
I'm sure if I had caught a murderer or rapist I would have felt different - because those arrests clearly result in getting a "bad" person off the streets. So, in that case, I can say that I would have felt great!
The thing I think I felt the best about was in being a visible deterrent and helping people to feel safe. Especially after 9/11, when people were afraid to fly. I worked at the airport, and, just being visible and taking action as needed made people feel safe.
Hope this helps!