Infrastructure: One of the major differences between Dynamics AX and Dynamics 365 is Infrastructure.  While Dynamic AX is implemented on an on-premises server, Dynamic 365 has its entire application program being operated on a cloud platform.  With Dynamics AX, you require having your own IT infrastructure, whereas with Dynamics 365, there is no burden of paying for extra infrastructure. You can also utilize this software from everywhere.

License: In Dynamics AX, you need to pay for everything related to the license before you buy the service. In Dynamics 365, you get more flexibility in payment options: monthly or annual licenses which makes it relatively cheaper.

User interface: You can use Dynamics AX on a desktop while Dynamic 365 gives you the freedom to use it on any of your devices. You just need a good internet connection on that device. Dynamics AX has a traditional interface that is not good enough but Dynamics 365 has a modern and clean layout. Anyone can easily navigate in that interface.

Integration: As compared to Dynamics AX, D365 can stand as a better option in integration. In D365 you can integrate Microsoft applications like Power BI, Teams, Azure, and others which are created by Microsoft partners. On the other hand, in Dynamics AX, customization is required to integrate applications, and you only get limited options in applications.

Updates: As Dynamics AX is more traditional software in comparison with D365. In Dynamic 365 you get regular updates and it can done automatically. While in Dynamic AX you have to manually complete the update process which requires large migration projects.