Twilio is the developer default worldwide and deserves the reputation. The API is the best-documented in telecoms, the SDKs are good in every language, the console is usable, and the platform extends into voice, video, verification, WhatsApp and a lot more. If you need one vendor for messaging across many countries, it's the obvious pick.
The problem for Australian traffic specifically is price and currency. Twilio's per-message rate to Australian mobiles is typically well above local aggregators', you're billed in USD with the exchange spread that implies, and its Australian presence is a regional deployment of a US company rather than a local entity.
ClickSend is an Australian company (Perth-based) selling SMS in AUD with local support hours. The per-message price to Australian mobiles is meaningfully lower, the API is straightforward REST that anyone can integrate in an afternoon, and you can sign up and send a test message without talking to a salesperson — which, in Australian telco, is a genuine differentiator and the killer field on our AU SMS hub.
If you send to Australian numbers and Australia is your market, ClickSend is the better economic answer and the difference compounds fast at volume.
If you send globally, or you need voice, video, verification and messaging on one platform, Twilio's breadth wins and the premium is what that breadth costs.
Plenty of teams route Australian traffic through a local aggregator and everything else through Twilio. That's slightly more code and considerably less money.