A grammar question, As or That?

Here's a sentence:" However, stress isn't the bad thing ＿＿ it is often supposed to be." Should I use "as" or "that" to fill in the blank? And how to figure out the difference?

Of course you can treat it in a more flexible way if you don't need to pass your exam ;)

Thanks a lot for your answer, Toby ;) I think I've understood it.

Thanks for correcting me, Toby.

Gucci Yeung, These sentences are probably acceptable:

Stress is not the bad thing (that) it is often supposed/thought/considered to be.
Stress is not as bad as it is often supposed/thought/considered to be.

http://grammar.quickanddirtytips.com/when-to-leave-out-that.aspx

http://www.usingenglish.com/forum/ask-teacher/40200-relative-adjective-attributive-clause.html

http://dictionary.cambridge.org/dictionary/british/as_1

http://www.bbc.co.uk/worldservice/learningenglish/grammar/learnit/learnitv158.shtml

Thanks for always answering my questions with patience, tiffintime. Happy New Year to you ;)