Do not move your current Roth IRA money. I hope that's not what you are asking, but it does kind of sound like it. That money has already been taxed and will not be taxed again, unless you are foolish enough to move it into your 403B.
I think you're really asking about future contributions. Guessing future tax rates is just that, it's a guess. That is the #1 factor though, if you can defer taxes AND pay less tax in the future than you could now, fill the 403b first. Does a 403b have an RMD at age 70 like a 401K or regular IRA? If it does, at $16.5K/yr + growth you might be surprised at the income you'll have in retirement. You can always convert some of it to a Roth in retirement.
There are other factors at play. You can invest that Roth IRA however you like, and at Vanguard you may have lower fees than your 403b. If you don't like your 403b choices, you might want to fill your Roth and contribute what you can to your 403b.
A Roth also gives you some flexibility if you would need the money in an emergency. I can't remember all of the rules but it is more flexible than a 401K. I think there are also some advantages with the Roth to your heirs if you should die early.
With today's tax laws, there's another advantage to keeping retirement income low, in that if you are in the 15% bracket, any dividends or cap gains that stack on top of your income but keep you in the 15% bracket are untaxed. Social security is also taxed less if you have less income. Money pulled out of a 403b in retirement is income, money pulled out of a Roth has already been taxed and is not income.
Always do the matched contribution first, but it sounds like you don't have one. I'd tend to go with the Roth next, unless you're pretty confident about your taxes being less in retirement. If you qualify for contributing to a Roth, your tax bracket can't be that high right now. Mostly 25%, possibly some in the 28%, right?