Assumption - I'm viewing each market as a whole - not taking into account specific neighborhood dynamics.
My brief observation:
In Los Angeles, the impacts of investing in rent-controlled areas are offset by consistent, appreciation % YOY (since 2012) - median home sales prices have increased by 64% from $393K in Sept 2012 to $644K in Sept 2017. It is not uncommon to see buy-and-hold investors take on negative/break-even cashflow properties, while relying solely on appreciation. The fix and flip market (especially for high-end, luxury properties) is so hot because wider margins exist.
In contrast, Chicago has seen median home sales prices increase 32% from $167K to $221K during that same time period. Cashflow is still possible in certain neighborhoods, but the projected appreciation is no where close to LA.
Unless Chicago experiences similar appreciation as LA, which I don't see based on pre-recession vs. post-recession median home sales price numbers, the implementation of a Rent Stabilization Ordinance will discourage investment from buy-and-hold investors, who will start to see a squeeze on cashflow (restricted rents w/rising property taxes) supplemented by sub-par appreciation gains. I see this having downstream impacts on the fix and flip market as well. This combination makes the Chicago market much less appealing.