Of you aren't maxing your retirement accounts a ROTH is a great place to park emergency fund money. You can always take the co tribute ones out, and the earning will grow tax free. If you end of not needed it for emergencies, it is there for retirement.
If t is emergency fund money I would be tentative about investing in mutual funds, but I am risk averse and have been burned when I needed he money and the market was down.

Definitely better to do Roth IRA because it's not that hard to get at your contributions if you need to. In general I would take any tax deduction you can get unless you think you might need to access the money before retirement.

Short question- does it make sense to invest in mutual funds if you are not maxing out retirement savings (401K/Roth IRA)?

Background- I’m taking a new position soon, resulting in a serious hit to our household income (and moving us within the income eligibility for Roth). Right now I max out my 401K and, in my budgeting for the new position, was thinking about moving cash currently in a conservative emergency fund to a low fee vanguard account, thus meeting the account minimum with the plan to contribute 3 to 500/month moving forward. (Uncertainty re: my current job had me holding on to more cash in the emergency fund than I feel I’ll need once I switch positions- we have a separate account for home expenses/car repairs).

But, it occurs to me that once I switch positions we won’t be taking advantage of all our tax-advantaged retirements funds. Would it make more sense to hold the cash and put it in Roth IRAs in 2015, and direct the monthly savings to the tax-advantaged retirement funds? It’s 5-10K in cash, so my thinking was that it would get us in to a low limit mutual fund and we could make small contributions thereafter, but now I’m wondering if that is silly if it is at the expense of potential savings via the traditional retirement vehicles.