I had ADT for 10 years when I lived in the city. I never had any problem with their service. I would presume Brinks is comparable in service. So, I would suggest shopping based on price and features.
I had a wired ADT system, but then wireless came out and I upgraded. I would recommend the wireless system with remote entry-- I loved that!
Do a comparison based on their package prices, features, and monthly service fee including cancellation/renewal fees/timeframes.
Also check with different affinity groups you may belong to in order to see if they have an affiliation with one or the other company. For example, I had homeowner’s insurance through USAA and they had a program with ADT for discounted installation and monthly fee. Perhaps your insurance company does too or some other group you are a member of-- a union, AARP, AAA, credit card company, credit union, etc.