First off you can use Traffic Manager, or VM Load Balancing, or you could actually use both! It all depends on what you are trying to do.
VM load balancing:
1.Works only with VMs that are in a single region
2. Only does Round Robin
3.Works at the TCP/UDP level, routing traffic between one or more private endpoints that sit behind a public endpoint
This is an excellent example for load balancing Virtual Machines.
Traffic Manager is different in that:
1.It can work across regions
2.It offers three traffic management policies round robin, failover, and performance
3.It works at the DNS level, sending the caller the DNS name of the endpoint where the traffic is configured to go given the policy.
This is an excellent example for planning your traffic manger Implementation.
So if your Virtual Machines are all located in a single region and you want to do Round Robin, VM Load Balancing is perfectly fine for you, but if you are located in different regions or want to use something other than round robin, Traffic Manager is probably the way you want to go.