I don't know about safer but I would think BA is cheaper. Although inflation is high in Argentina and that may tip the balance. Wherever you go, I would suggest you learn a few basic Spanish phrases and buy a phrasebook. It really will make life a lot easier.

I would say Santiago is safer and, due to inflation and other factors, about the same price as Buenos Aires. There is a reciprocity fee flying into Chile for some nationalities but a lot of hotels will not charge you the sales tax (19%) as a tourist. Eating in BA is still very good value.
Having said that, I would urge you to base your visit on other criteria. Greater Buenos Aires has about the same population as all of Chile. If you want big city buzz and nightlife, go to BA. Santiago cannot compare. If you like the outdoors, choose Santiago where you can get to the Andes or the beach or vineyards in under 2 hours.
Do a little reading up on both and decide which one appeals to you more. In both cities it is possible to do an economic visit if you plan and I really wouldn't make cost the main focus of your choice.

BA is a far superior city on many fronts than Santiago.

Crellston:

My wife and I were in Santiago once and Buenos Aires four times.

If I were planning my next trip to South America it would be Buenos Aires hands down.

As already noted in the posts above, what you get for your dollar is more important than how many dollars you have to spend.

My personal feeling is that there is more and of finer quality in Buenos Aires than in Santiago.

I like to get good food. Santiago on the coast is better for sea food but Buenos Aires is better for steak, pasta, empanada and pastry.

As advised, read up on both places then you will be better informed to choose what appeals to you rather than what appeals to everyone else.

Safety? I found both cities safe enough. Take the usual precautions. Digital camera and cell phone theft is on the rise. Don't stop in one spot taking pictures for a long time and be careful in the usual 'tourist' spots and at night in lonely places. I don't use a cell phone so I can not advise on that.

Woodie

Chile is a wonderful destination, but head to head Santiago and BUenos Aires, or BUenos Aires and Montevideo ...Buenos Aires wins by a landslide,Bs As is a great city, may is not what it used to be., and of course safety has been re written all over the world,
Some twenty years ago when I used to live in Buenos Aires with my family any woman could
go to a late movie , let us say in calle Lavalle, late at night and walk back home.
Now.... I do not think it will be wise.

Graziella, I was in BA last month and we walked around until 7am. It is still perfectly safe.

Soulskier, you're saying "we walked", so I'm not sure if you were a lone female walking.

They are a married couple, WillTravel.

http://livinginpatagonia.com/?page_id=2

I walked in BS AS with my 12 yo son and felt very safe at all times. When travelling alone in Italy I was robbed twice with certain violence so I learned my lesson. I carry a small money holder with a small amount of money concealed under my jacket. I never carry a hanging purse or anything of value and I leave my credit cards , tickets and passport in the hotel safe. I never stop to read a map, I try to memorize the map before I leave in the morning, I walk fast as the locals and try not to look hesitant even if I am lost. If it is sunny I wear dark sunglasses to avoid eye contact. If I need to ask for directions I go inside a kiosk or store. If you have to walk alone at night, try to walk on a very well lighted street where you see other people, if you don't know the neighborhood is better to get a cab by radiollamado. It is also useful to know the language. I hope this is helpful and have a good time in Bs As.

I am so pleased nothing happened to either of you ( Carlimusa and Soulskier). I did not mean that walking per se in Bs AS is dangerous. I meant that years back for a woman alone, or two women...leaving a late movie that is aprox midnight and walking home, a reasonable distance, was done all the time.
To-day I do not believe that the conditions are the same. But again if nothing happened that is great, however, sadly, I still believe it is not safe.
( I have lots of friends and relatives in BS AS)

I did walk back a couple times late at night when I was staying right at Florida and Corrientes, so I was basically on busy streets the whole time. I did see homeless people, but did not feel threatened.

I had a strange experience with a man following me for several blocks around 5:30 PM in Microcentro. Luckily, I guess, I wasn't able to understand him at all, although he kept trying to communicate with me. But it was too noisy, or something. He was very well-dressed and actually good-looking, but it was nonetheless offputting. This was on my last full day in Buenos Aires. (My belief is that he was probably an Argentinian gigolo seeking a North American woman, as unwealthy as I may look, but I imagine other theories are possible.)

Of course I had also heard about these events with people getting sprayed, so that made me nervous. If that happens reasonably often during the day, as it seems to do, I can't imagine it's a great idea to be walking around too much late at night.

having just been to both, i would pick b.a. hotel prices are about equal but food costs seemed much cheaper in b.a. also if you are younger i would think you will find palermo and recoleta areas must more interesting.

Hands down, no question about it (been to both): BUENOS AIRES! I loved it so much I bought an apartment there!

Reading the answers it is easy to realize that you can compare pears with apples.No offence to Santiago but Buenos Aires is a much more interesting destinations
any day.