From what I can see, and I do have a Sharesies account , though not a Hatch one - but I read their website - the differences are not that great. But Sharesies has an ongoing fee , so a large static portfolio would be better to have it with Hatch where the fees are transaction based (apart from a 50c a year fee for tax returns) not portfolio size based.
I quite like Sharesies as a tool for novice investors to get into the markets. Hatch of course provides a US specific service and so would offer a much wider range of investments as well as more specific investments for well-known companies eg Tesla or Disney shares however small investors as you say you are should probably be sticking to ETFs so they can obtain diversity. But if you want to take a punt on say Uber or Airbnb shares then Hatch provides a way to do that. Hatch says they offer 2900 individual shares and over 500 ETF. Plenty to choose from compared to Sharesies. Its a great option for Kiwis to have, thanks for drawing it to my attention.