I’ve worked for both, but have spent most of my working life working for Christian organisations. This wasn’t a deliberate choice by me (although probably different for God) - they just offered me a job at a time when I was looking for one. I have no real preference for either, but think that it’s important for Christians to work in the secular workplace, both in order to gain skills which can be used to God’s glory, and to maintain connections with non-Christians.
I can also think of two main disadvantages that may come from working for a Christian organisation.
1) Your colleagues will eventually disappoint you. Even if everybody on staff has every issue of the Briefing and has a tattoo of Peter Jensen, they are still sinful, and will eventually act in ways that will disappoint and/or hurt you. For some reason, we don’t expect such behaviour from our Christian brothers & sisters, and so the disappointment is greater.
2) Dodgy theology In the first Christian organisation I worked for, one staff member was so enthusiastic about the Toronto blessing that he travelled over to Toronto to get it, and enthusiastically promoted it at church and work. And in my current job I’ve had to deal with an organisation that was originally evangelical, but at its’ nadir was totally dominated by the social gospel. It was difficult to be enthusiastic about working at a Christian organisation in this situation, despite the good work it does. (Fortunately, I believe that things have improved somewhat.)