I see tenant screening in two different ways:
1) independent services, just like Exeprian, Tenantverification etc. They are specialized only on tenant screening with all credit and background checks, reports. Mostly, it is paid, but in general - fast and high effective.
2) services that are included in sites, that provide rentals for landlords and tenants just like Cozy, MySmartMove etc. It is what you mentioned.
For my personal use, I tried Cozy, SmartMove, the best one for me is Rentberry's tenant screening because it connected with Experian, it's free and it's a great deal you know. Because I really did'nt find anything that may be so simple and ready for use as Experian. Try it if you want.