What advantages are there to operate a corporate flight department under Part 135 as a separate entity instead of in-house as a Part 91?
There is no reason you can't operate as a part 91 department but simply adopt the standards of 135.  Government contracts work this way.  It's all pt91 work but adheres to pt135 rules.
Actually holding a 135 is a lot of work and is expensive.  The training and checking requirements are onerous for your average flight department.  How do you feel about potential career limiting checkrides every six months?  You also need to keep the planes up to a higher standard.  This means observing TBO hours and calendar times.
You don't mention aircraft types, but Continental requires piston engine overhauls at 12 year intervals or upon reaching the time limit, whichever is first.  Even a piston single becomes expensive to operate.