When you pay using Australian dollars, the bank will exchange it at a pretty decent rate and then add the international fee of about 3%. So, when I booked my Book of Mormon tickets in USD it was $534.24, which came to $580.60 plus $17.40 conversion fee - a total of $598.
If I had charged this on my travel card, I would be charged the conversion fee at the time I put the money on my card, instead of at the time of purchase. For my Load and Go Travel card the rate is therefore about 4c different - if I were to put $1000 AUD on it when the exchange rate was 94c, I would only get $900 USD. So if I had put money on my card then booked my tickets that same day, I would have paid about $602. This is based on just adding 4% to the rate the bank used, but it was probably a smidge lower than that. Basically I would have paid the same amount either way.
However, if I loaded the money onto my card when the rate was better, then I would have locked in the money at that rate, meaning I would have saved money by using the travel card. So, just say it was 1c higher when I loaded it, the tickets would have been $596.
On the other hand, the rate might have been higher when I loaded the card than when I booked the tickets. If it was 1c lower, then the tickets would have been $607.
Alas, without a crystal ball or time machine, it's impossible to say what is going to be best!