What is the difference between "面对" and "应对"?
To answer your question, "以。。。的太对(态度)来应对／面对 这个问题 ？". If you want to stress on the attitude (positive, negative, responsible, etc), you should use 面对. But if you want focus on the action strategy, then it's 应对. 

以积极的态度来 应对 这个问题 -> to handle the issue with positive attitude (we should not wait here, it's not the end, let's do something!)

以积极的态度来 面对 这个问题 -> thinking of the issue with positive attitude (it's not so bad, we still have chance, let's more focus on the bright side)

面对 is usually used to describe a situation. Here 面 means "facing -> regarding to".

Meanwhile 应对 is more focus on taking action. 应 means 响应 (respond), 应付(deal with).

One example can be found here: http://jingyan.baidu.com/article/6b97984d9dadef1ca2b0bfe0.html

面对 危机我们该如何有效 应对

How should we respond effectively (regarding) to the crisis

You can find more similar cases by searching both words: http://bit.ly/1nRji4a