My Mum went out in 1958 to try to persuade her sister to return! She always wanted to come home (her sister didn't) but it took 8 years as she married an Aussie (my Dad) and brought him back! She said the boat over was rough as guts and that Sydney was not exactly like the ads at the time. You can see these short films and ads on youtube which I think were played in cinemas etc showing a perfect life, sunshine beaches etc. She said Sydney at that time was a different place to the international city it became later. Basically a rough port in the middle of nowhere. Letters took ages, phone calls cost a fortune, no news or papers from home, a bit behind. Affordable outer suburbs in the 50's where most migrants settled were a long way out, a long way from any beaches, mostly 'fibro' cottages with semi dirt roads and outside dunnies with spiders. No air conditioning in homes, buses, trains, offices, shops, etc. Circular Quay and Darling Harbour were still industrial, miles of wharves, coal loaders for the power stations on the harbour, dirty and so not the shining place you see today, no gleaming office towers or Opera House back then.
Naturally with any big intake of migrants locals could be a bit off: They're swamping us, they're taking our jobs, they're cheap with cash, they don't shower, silly accents and expect to live like they did in their own country, whinging that it's not as good as Britain, they crap on about their English pubs and football, who do you think you are, go home if you don't like it, etc etc (ring any bells?)...
My parents have obviously been back many times since and love Sydney saying it is transformed now and not the place they knew and of course the world is now super connected and the journey is 24 hrs and a credit card, not a year of saving and 5 weeks on a boat.
I guess everyone's experience will be different. I think this will be the biggest reason for staying / returning. Your feelings will be shaped by how good your job was, where you lived, who you met for friends, if your neighbours or workmates were good, how adventurous or open to change you were, if you missed people at home etc. Any massive life change is shaped by these day to day things and your expectations v reality just like today.
Even now for people making the change (which I did 30 years ago) it's good to understand that it's not Britain in the sun as advertised. It is a different culture, people might look the same but they think differently. Sport still rules over inside pursuits like books, music, art. It's very multicultural in the cities which are huge & much more American that the UK and the standard for everyone is to leave your old crap behind, get on board & live optimistically for the future no matter who you are. Migrating to a new country & settling wasn't an easy ride then and still isn't unless you're ready for some years of adjustment & 'starting again'. I've know people in my time that have flip flopped between Aus and England. Both places are great but ultimately you have to choose one or the other!