Can't Make Sense of AUD vs USD and EUR Exchage Rate

USD gained some ground recently and USD > AUD is currently trading

2013 Jul at 1.08
2016 Nov at 1.31

but the EUR > AUD rate remained the same

2013 at 1.41
2016 at 1.43

while pair EUR > USD is trading

2013 at 1.30
2016 at 1.06, almost 30% difference

How is this possible?
And what currency is better to spend TODAY if you have cash USD and EUR and live in Australia?

You may want to brush up on your maths first.

$-Euro on 17/11/13 was $0.7417
yesterdays average was $0.8987
difference of just over 21%

$-Aud on 17/11/13 was $1.0673
yesterdays average was $1.3216
difference of just over 23.6% (closer to 22.5% using your figures)

Not such a big difference after all, besides which currency pairs are not tied to one another in such a way that prices exactly correlate.
Regarding your question, surely if you live in Australia you have to spend in Aussie dollars, unless you are buying products from overseas in which case either the local currency or, frequently, US dollars are acceptable

Use myfxbook pair correlation data for better understanding Forex Correlation | Myfxbook

Nice link!