Your NZ passport may provide you with better visa in Britain. Particulalrly if you have a Grandparent from Britain which enables you to get a three year ancestry visa. Both countries are friendly but would say more could go wrong in London with lots of petty crime and hooligan type behaviour in certain areas. Britain generally has a much bigger market for short term, tourist related jobs. Working in a pub where you get lodging and breakfast provided plus a smallish salary was common practice in my first visits to the UK. London is very, very expensive though.
Canada is absolutely beautiful country, particulalry in Autumn. Working there is likely a bit more difficult (not sure on this) than Britain because the tourism industry is not anywhere as big. But you would get a waiters job no problem I would say. Summer time in Canada has more seasonal tourist related jobs so much more difficult to get jobs during Winter.
I have lived in Canada and toured Britain many times. In simple terms Canada will offer great wilderness and exploration plus very hospitible Canadians. Modern cities - I really like the french influenced Montreal. Britain offers great history and European influenced culture plus huge opportunity to meet all types of people. Would say you will have a much wilder time in Britain than Canada but have no idea how this would interest you. Enjoy your travels. Great to get the broad minded worldly view as a youngster. You will likely catch the travel bug and be gone for a long time once you get established.
The UK economy is doing quite badly right about now, so I suspect getting a work visa there would be quite difficult. In general for either Canada or the UK you'll likely have a much, much easier time getting into the country off a NZ passport than a Ukranian passport.
I love Canada
Never been to England.
Both are excellent choices.
Avoid the U.S.A you could get shot.
Canadians are very ease-going and hospitible . ukra and nz are quite different passps. finding job in canada is not difficult .
england is better choice