There are a number of important differences between Microsoft Dynamics CRM 365 on-premise vs online. Each model should be carefully examined in deciding the greatest model for your big business. Microsoft CRM on-premise was released in 2003 and went through several versions (1.2, 4, 2011) before the online model was released in the 2013 version.
The online version is a true cloud/Software as a Service (SaaS) application. It is a multi-tenant design meaning that multiple companies use the same infrastructure (it is not dedicated to one company). One major difference, as a result, is that you do not have direct access to the SQL database. To access the database you use fetch XML and API calls vs SQL queries. This can be a learning curve for those used to direct SQL access.
Another significant difference is in PowerBI. The online version fully supports integration with Microsoft PowerBI and it is easy to setup the connection. The on-premise version of Dynamics CRM 365 can connect to PowerBI but the process is much more involved.
Cost Comparison between Microsoft Dynamics CRM 365 on-premise and online
After 6 years of talking to companies about the price comparison between online and on-premise, I explain it like this:
Dynamics 365 Online average subscription cost. $80/user/month (average between the Sales Enterprise $95/user/month and Sales Professional $65/user/month. So let's take a 20 user deployment, the monthly software subscription cost would be $1600 or $19,200 per year, $57,600 over 3 years.
The on-premise licensing is a perpetual license model (you buy the licensing and own it forever). The cost of an on-premise license is $2,873 and comes with 3 years of maintenance (software assurance). So for the same 20 users, the 3 year license cost would be $57,462.
It's a wash BUT now consider the capital investments in infrastructure and IT administration over 3 years for the on-premise version. This will be different for each company as some will have a virtual server environment where the upfront infrastructure costs would be less.