it would be wrong to assume that old world vines are always older than new world vines. the effects of phylloxera and changing market demands mean that many old world vineyards are recently planted. on the other hand, some australian wines are produced from 100+ year old vines.
the difference in wine styles is, i think, more a factor of culture, economics and climate. some boutique vineyards in cooler australian regions produce sophisticated wines that you might find interesting. many new zealand wineries produce complex and sophisticated wines. but it can be hard to find these and you have to pay a premium.