Aas long as you leave a country with the same passport that you entered in on, then you're ok.
So: Option 1:
Entering Aus on Aus passport, leaving on Greek = bad Option 2: Entering on Greek, leaving on Aus = bad Option 3: Entering and leaving on Greek passport = good Option 4: Entering and leaving on Aus passport = good
The reason being for counts and tracking - if a Greek tourist has entered Australia, but has not been seen leaving, panic ensues (well probably not, but that's the theory anyway).
That passport has 'overstayed'.
And you NEVER want to get pinged for overstaying.
Once you've left a country, meh, they no longer care about you.
So when you come back to the UK, you can use whatever passport you want, so long as that passport has the legal entitlement to work there (if you're working there).
Greek passport is obviously easy for this, but the Aussie one you'll require a visa of some sort, if you present that at the border, as you're now being treated as a non-EU citizen (as that's the passport you chose to present).
Hope that makes sense.
travel.stackexchange.com/users/101/Mark Mayo
Definitely you should use your Australian passport in Australia and Greek passport in Greece (because for these countries you are their citizen and they don't really care if you have a dual nationality).
And as others have said it's safest to use the same passport to enter and exit the country.
However, in many countries the police would not check your passport on exit (I don't think anyone checked my passport when leaving the UK), so this discussion might be a bit academic.
travel.stackexchange.com/users/44/Grzenio
A few searches through this site will discover pairs of countries that don't like to see each other's stamps in your passport.
If you plan things right, you can use separate passports to make this less of a worry for you.
For example you might use one passport for Israel and the other for all the countries that might not like seeing an Israel stamp, or whose stamps might raise eyebrows when you go to Israel.
I don't know what the collections of countries are these days.
When I was a child my father had one set of countries including USSR and Cuba in one passport, and another set including the USA in the other, and he had a much smoother travel experience than his colleagues with only one passport.
Also, you can choose the shorter line most of the time when you're interacting with a neutral country and don't care whose passport the stamp goes in.
Or if you need to send your passport away to get a visa in it (still happens)
you can travel on the other in the meantime.
Plenty of advantages
but you will do best if you plan a little in advance.
travel.stackexchange.com/users/46/Kate Gregory
As long as you leave and enter on the same passport it is fine...
for instance I have a South African and Swiss passport.
Leave and enter SA on my SA passport and enter and leave Switzerland on my Swiss passport.
No hassles!
It does seem weird but for all the country cares you haven't left an airplane the whole time!
travel.stackexchange.com/users/1096/nicV
I have dual nationality (UK - Australia), and I always show both on departure.
This stops them getting worried that they will have to deny me access to the flight because of visa issues.
They should still only use one of them (the 'local' one) for their record keeping though.
On arrival I just show the local one as that is less hassle for everyone.
travel.stackexchange.com/users/987/NWS
I plan to visit Australia from the UK, I am an Australian national with dual nationality - I also hold a Greek passport.  I have all the correct documentation and everything is fine.  However, if I leave the UK and present my Australian passport to immigration control on exit from Heathrow, will this then pose problems when I return back to the UK and present my Greek passport. I will be carrying both passports.
Dual nationality, EU and Australian. Does it matter which passport is "travelled on"
travel.stackexchange.com
<customs-and-immigration><passports><australian-citizens><eu-citizens><dual-nationality>
travel.stackexchange.com/questions/3085
travel.stackexchange.com/users/1021/NimChimpsky
Aas long as you leave a country with the same passport that you entered in on, then you're ok.  However, you should probably use the passport of the country you're visiting if you are a citizen. Entering and leaving a country using the same passport is considered the best travel advice. However, if you are visiting a country you are a national of, use that passport. It may be a good idea to show both passports on departure to avoid visa issues.
Enter a country and leave using the same passport. Use the passport of the country you are visiting if you are a national. Show both passports on departure to prevent visa issues and local passport on arrival.