Hi,
Differences are big, but let me try to describe them a bit.
1. Cisco ACI with VMware VDS Integration
When integrating VMware vSphere Distributed Switch with Cisco ACI, the VDS enables you to configure VM networking in the ACI fabric, through the use of EPGs. Basically, you create an EPG-port-group mapping.
Since the use of DVS in vmware is very common, this VMM integration is one of the most deployed and easy to adapt in ACI.
Details about how to configure: https://www.cisco.com/c/en/us/td/docs/switches/datacenter/aci/apic/sw/3-x/virtualization/b_ACI_Virtualization_Guide_3_0_1/b_ACI_Virtualization_Guide_3_0_1_chapter_011.html
2. Cisco ACI Virtual Edge
Cisco ACI Virtual Edge (AVE), on the other hand, is a hypervisor-independent distributed service virtual machine (VM), that operates as a virtual leaf, running in user space. AVE is specifically designed for Cisco ACI, and is managed by Cisco APIC.
A very common use case for AVE is when your workload is not directly connected or maximum one L2 hop away (requirement for VDS integration) from your ACI Leaves.
Another scenario where you might want to use AVE, is if you want to have full visibility of traffic switching in he virtual infrastructure (plus you have extra data through telemetry).
Last but not least, you can run vxlan between AVE and your ACI infrastracture, leveraging infra VLAN.
More details about AVE:
https://www.youtube.com/watch?v=tEtMhJKnwRM
However, because the learning curve for AVE is more steep compared with VDS integration, and troubleshooting it is more complex, I would suggest to stick with VDS.
Regards,
Sergiu
