I guess it depends on what type of instruments / securities and in what regions you plan to be "trading" in. It is in my opinion that the NZ Stockmarket is not particularly suited for short term trading due to the comparatively low liquidity and high brokerage fees.
ASB securities seems to be geared towards more for investors wishing to invest longer term in the NZX and perhaps the ASX as well. Using ASB Securities to trade in any other market (outside Australia / NZ) is not particularly cost effective (Buying and holding Stocks in say the US I believe is very expensive through them). Not sure if it's the same with Direct Broking.
I will state upfront that in my opinion in general terms, I'm somewhat unconvinced / reticent about short term securities trading as far as doing it as an individual punter goes (on the retail level) especially with minimal capital (say less than 100k)
If you still want to try you hand at short term Trading, you may be better focusing on much bigger markets such as the of the US and set yourself up with an US brokerage account that is geared towards active short term trading. I think there may even now be brokers that allow people to access several different markets across different regions for trading (but I don't think any of them are based in New Zealand).