However, you can look at the tax rates within Cook County and even compare them to the suburban counties [1]. The composite property tax rate is as low as it gets around here. Most cities are double or triple the Chicago rate.
It isn't as good of a deal as when I moved here, but if you've got a tech or other white-collar salary, Chicago is still a really good deal. It's your responsibility to consider cost when choosing a location within the metro area. If you ignore it, you shouldn't be surprised that you pay more.
[1] https://www.cookcountyclerk.com/service/tax-extension-and-ra...
EDIT - Illinois and Texas heavily depend on property taxes for local funding. The actual rates you pay have an insanely high variance from city to city. Some taxing districts don't align with city boundaries either, so one neighborhood may pay more than another. You can use it as a proxy for how well-run a city is, but on the other hand Chicago isn't a particularly well-run city - it just has a huge amount of high-value commercial and industrial property (which is taxed at double the rate of residential property). If you're going to live in either state, you really need to look at the hyper-local tax rates and put that into your decision matrix. The data isn't even hard to find.