For those of you with experience in both, civil and military projects.
Are there specific software engineering traits that usually shows up more often within military projects?
I mean things like paperwork, language of choice, management hierarchy...
Wikipedia's page on MIL-STD-498 and other DoD/MoD software standards might give you some idea.
See the Defense Acquisition Guidebook and DoD Instruction 5000.02 for a detailed description of the current DoD acquisition process. The DAU wallchart attempts to summarize the process in one poster.
In general in a military project, you will have no choice of tools and very little flexibility. They have detailed standards which must be met. Since many military software projects involve some level of classified data, you may also be very restricted on whether you can work through a VPN tunnel or how much you can share with others. Posting snippets of your code to a site like this would be frowned on. Agile methods are often frowned on as detailed requirements must be approved. This may have changed since the last time I worked with the military, but I doubt it. The miltary is a very large, very beauracratic organization (at least the US military is) and that isn't going to change anytime soon.