I've lived in BA and visited Santiago twice for short times.
In my experience, Santiago has more pros than BA. The economy is doing well, the government is progressive and the transportation system is good. If you do visit both cities, ride the subway systems for example. Getting in and out of Chile is also easier now that
immigration rules have been relaxed. It's easy to travel over to Argentina to renew a visa if you need to.
Santiago seemed safe enough for me and I never ran into trouble walking the streets even at night. I was a bit surprised with the people because they were friendly and the mood was good toward foreign people. In BA, the attitude is that if you don't like something, you should leave. Go back to your own country. You're not Argentine and you never will be. Looking back on it, I see it as a form of racism. The government is a partner in that, allowing for a two-tier pricing system on everything from Airline flights to national parks.
The economy in Chile is doing well and seems to be one of the most stable in SA. Prices in Chile are higher and I expect the cost of living would be more. Argentina has a devalued peso but is now in the early stages of
hyperinflation, even if the government denies this. Tragic mistakes and corruption with the government are taking their toll on the infrastructure.
Both cities are very elegant with BA having more to see and do on a surface level. I prefer the food in Chile. For language, the spanish in BA is a unique form that's really only good for the city. In Chile, they speak quickly but the spanish is more transferable to other regions and countries.
Severe pollution is a problem in both cities and both suffer from bad weather at certain times of the year. Santiago has the misfortune of inversion because of the mountains close by although this problem has been slowly getting better. When I was there, the air was good and noise pollution was certainly lower. Like other posters have mentioned, Vina del Mar is a better choice if you don't have to live in Santiago for a specific reason. Also to the west of Santiago heading toward the mountains is nice.
Regarding the women, I was surprised how attractive the women in Chile are. They are more conservative though. Both cities have a booming inexpensive sextrade even if prostitution is supposed to be illegal in Chile. Argentine women are attractive as well but that's a taste thing. Personally, I got tired of the BA women pretty fast and the Chilean girls were a nice change. I also visited places like Vina del Mar which is a beach community and all that goes along with that.
Keep doing research and read what people are saying in forums like this and others. It's a good way to get overall impressions and also learn in advance. Look into international banking and if that's possible.