I voted for Stern. Investment Management on its own is an unstructured recruiting cycle (compared to IB, Consulting, etc), so you will need all the help you can get.
I am sure both schools give you access to the biggest asset managers out there, but there is so much more that Stern and NYC can offer (specialized funds, Hedge Funds, smaller AM, etc).
Therefore, networking will be key, and Stern wins here hands down with all the alumni in the industry. Most of the alumni is in Finance, and access to other non-mba alumni such as part timers (already in industry), Stern undergrad alumni, etc. Additionally, finance Faculty at Stern is amazing. Anyone can only dream of taking a class with Damodaran.
In terms of culture (I did not apply to Haas, so not much I can offer there), but Stern has an amazing culture I did not expect in the heart of NYC. Hate to say it, but their culture is way better than Columbia's. And their EQ+IQ mantra is very real.
Thats my take on it. I got into Stern last year, I did not take it. I went to another program (currently a first year at an M7, and Stern was really hard to turn down). I am recruiting for IM, and have gotten to see the success Sternies have had in the field.
Best of luck! Stern is top 10 in my book, top 3 in Finance for sure!