The major advantage, IMO, is that you have many more options in an IRA than you generally do in a 401K or 403b.
I know DP's employer provides approximately 15 investment options within his 401K. Meanwhile, in an IRA you can choose from basically any stock, bond, mutual fund, even some real estate.... just WAY more options and WAY more personal control!
Your savings are already tax-deffered (I think a 403b has the same tax benifits as a 401K which are both taken out *pre-tax*) so that is not an additional bonus, but you will need to consider if you want to keep it that way (ie Traditional IRA) or if you want to pay the taxes now and eventually roll it into your Roth IRA (which I would tend to, basically for ease of investment). Either way, you will need to first roll into a Rollover IRA.
Vanguard should be able to walk you through it. Make sure you have all your steps planned out in advance because you don't want the money actually withdrawn (rather than Rolled) because you could end up owing significant taxes and fees.