Installing Civi as a standalone site vs part of your existing site
If the CiviCRM is installed on a different Wordpress site, important features and functions would be completely crippled by not being connected to the front-end website:


Letting users input and manage their own contact information either deliberately or through contribution and sign up forms
You wouldn't be able to take donations through the CiviCRM through the front-facing website
Users wouldn't be able to sign up for events or memberships and be managed through CiviCRM
You wouldn't be able to collect user email addresses or get newsletter sign ups through the front-facing website to be managed through the CiviCRM.
Staff would have two different company websites to sign into for managing different things, instead of just one 


I can't think of many pros for doing it this way. Even if there are features you aren't planning to use now, you might want to grow into them.