If it is a once in a lifetime trip, then you could do a bit of both. But there are things to be aware of:
The time of year you come matters. Winter (here) will occasionally shut some passes between the two countries. Santiago/Mendoza is an amazing crossing through the Andes, but can close due to bad weather in winter. Lots of bus choices on this route.
The north of both countries is warmer in winter and there is lots to see.
A flight to see Iguazu is worth it.
Distances are huge. If you want to visit several areas, flights are sometimes a must. You can lose precious days on a bus.
Overnight bus can mean you get on in the evening and off for breakfast, but it can also mean you get on at night and arrive late the next day (or after!). Check how long bus trips take.
Buses in both countries vary from the good to the luxurious.
Buses between places often don't go every day: San Pedro de Atacama to Salta, Patagonian crossings.
Canadian, USA or Australian? Both countries now have reciprocity fees but only flying into the capital city. Land borders and other airports are free.
What you like to do matters. Buenos Aires is a superb urban destination. Santiago much smaller but has its charms. Both offer a lot of outdoor activities in various places. Fish and seafood in Chile, steak in BA.
Patagonia on both sides of the border is stunning. Not so easy to do in winter (June/July/August). Some transport and lodging closes down.
Build in some buffer time if going to Patagonia. Weather and breakdowns in transportation can delay you. Never plan to get from somewhere out of town to your point of departure for your return home on the same day.
Santiago has one airport which serves both international and national flights. BA has two. International at Ezeiza and national at Aeroparque (not their official names but what people call them). Aerolineas Argentinas is moving their BA to Santiago flights to Aeroparque (1 March 2010) although they are international flights. Check which airport you will arrive/depart from.