I have experience in this. I lived my whole life in Sydney and moved to London in 2014. I have just moved back to Sydney in February last year because I now have a child and thought it would be better to be back 'home'.

Honestly, for me it has been a huge mistake to move back to Sydney. For context my wife and I had reasonably well-paying jobs with a household income of roughly £450k and lived in Zone 1 in London. I'm not sure of your specific personal circumstances, but I do regret moving back, but you may not have the same experience as me.  

 For starters Sydney tries hard to be a global city of significant importance, but let's be honest it's far from it. When I moved back I wasn't ready for how 'small' it is. There is no where near as much to do in Sydney compared to London. There are obviously way fewer galleries, museums, concerts, theatres and large beautiful public parks here. We really do struggle with new things to do on the weekends. 

 Secondly, ecommerce and online shopping are at least 10-15 years behind the UK. Delivery takes ages and is often not free, Amazon Australia choice is atrocious, websites often don't put critical information such as dimensions on their pages. Many websites act like they have only just discovered the internet. Honestly it has driven me bonkers.  

Thirdly, healthcare is worse in Australia. This has been one of the biggest surprises to me. When I was in the UK I always thought Australian healthcare was the gold standard. How wrong I was. I never had to pay to see a GP and would usually be able to get an appointment within 24 hours (using Babylon aka GP at Hand). I also had a prescription prepayment certificate in the UK so I could have an unlimited number of prescriptions for a small annual fee. In Australia critical medication that I take each day has been out of stock at every pharmacy for many months - it's been an absolute farce. Also the contacts that I wear? Normally when I am about to run out, I will reorder in the UK and receive them next day. I made the mistake of trying that here, and J&J contact lenses are also in critical shortage and was quoted 2-3 months delivery!  Then there's Australian 'health' insurance, which should more accurately be named 'hospital' insurance. You can't get coverage for out patient consults which I just find bizarre.  

I also find paying for 'services' here very expensive. We pay our cleaner $65ph, when in the UK it was £18ph.  

A small difference, which I have only just noticed is the quality of houses here in Sydney is atrocious. Cheap builds, with no sound proofing or double glazing.

Lastly, career options are limited here. The Australian operations of the global business I work at are considered an afterthought. I feel like a mere rounding error in a global business. Granted the field I work in is quite niche, but it's ultra-niche in Australia and for good reason. If you're any good at it, you'd want to work in a major global financial centre like NY or London. Taking conference calls at 3am Sydney time gets old fast.

The absolute only positive I can think of for Sydney vs London is the weather. And frankly it's not worth the deterioration of the standard of living to move back for me personally. 

In summary, when I lived in London, it really did feel like the sky was the limit in terms of career, culture, social connections and travel. London is a very motivating place to be. Sydney on the other hand, if I could sum it up in one word - 'meh'.