The verdict
If phone calls drive your leads and you spend money on ads, I'd pick CallRail. Your ad platform cannot tell you who called, and that is half the picture.
If your leads come through forms, signups or a webshop and conversion has dropped without a clear reason, I'd pick Contentsquare, as long as the site has real traffic. For a small site with no one to act on replays, a free tool is enough.
They rarely compete. A service business with a busy site could use both. Choose the one that matches how your customers first reach you, and treat the other as a later addition.