Whilst Telstra's domestic coverage is undoubtedly better, I'm not sure how they compete abroad. Especially in countries where Vodafone has a presence or a large partner.
This has always been the irony of Aussie telco scene. Telstra has the most extensive Australia network but has the worst overseas roaming deals and has no real partnerships of note, while Vodafone falls short of Telstra's Aussie coverage but has the best roaming deals and a solid web of partnerships through its parent brand.
FWIW: I've been on all three telcos for varying lengths of time, but a few years ago switched from Telstra to Vodafone with the introduction of $5/day roaming – for obvious reasons my work involves a lot of international travel on business, so keeping connected is a
must (for basics such as calls from AU and locally, through to filing stories) and while I'd built up a little collection of SIM cards for each country, the necessary recharging was often a hassle and of course meant I couldn't be contacted on my Aussie number. Vodafone's $5/day roaming is
brilliant value for me, so much so that last year I took advantage of a special promo of free roaming on contracts $100 or above (no $5/day!), so I re-up'd the contract from my $80 plan, figuring that if I spend more than four days overseas (in a $5/day roaming country) each month (which I always do) then I'm ahead.
That said: I couldn't have made the move if Voda's Australian network hadn't improved from where it was quite a few years back, back when the issues where both coverage and speed. Sitting at a cafe in Crows Nest at 10.30am on a weekday, trying to pull email on your BlackBerry and having basically zero connectivity - that's not how these new-fangled wireless contraptions are supposed to work. These days I have Voda at 4G pretty much everywhere I go – admittedly my domestic pattern is one of cities, and in Sydney that includes the north shore and inner-west.
But it really comes down to if the network covers where you need to be. If I spent more time in regional areas, in the country, then it'd be Telstra for me, without a doubt. But for where I travel and what I need, Voda works a treat.