Compared: Azure Load Balancer, Application Gateway, Traffic Manager

The following table summarizes the features offered by each service:

Service	Azure Load Balancer	Application Gateway	Traffic Manager
Technology	Transport level (Layer 4)	Application level (Layer 7)	DNS level
Application protocols supported	Any	HTTP, HTTPS,  HTTP/2 & WebSockets	Any (An HTTP endpoint is required for endpoint monitoring)
Endpoints	Azure VMs and Cloud Services role instances	Any Azure Internal IP address or public internet IP address	Azure VMs, Cloud Services, Azure Web Apps, and external endpoints
Vnet support	Can be used for both Internet facing and internal (Vnet) applications	Can be used for both Internet facing and internal (Vnet) applications	Only supports Internet-facing applications
Endpoint Monitoring	Supported via probes	Supported via probes	Supported via HTTP/HTTPS GET
Health Monitoring	TCP probe HTTP probe	HTTP probe HTTPS probe	TCP probe HTTP probe HTTPS probe
Source IP/Sticky session	Supported, 2- or 3-tuple source affinity	Supported, cookie-based affinity	Not Supported
Traffic controls	Network Security Groups	Network Security Groups	Geo-traffic Restriction

This slide from the Ignite 2016 – Microsoft Azure Networking: New Network Services, Features And Scenarios session summarizes it well

click on image for enlarged view

Traditional load balancers operate at the transport layer (OSI layer 4 - TCP and UDP) and route traffic based on source IP address and port, to a destination IP address and port. But with the Application Gateway you can be even more specific. For example, you can route traffic based on the incoming URL. So if /images is in the incoming URL, you can route traffic to a specific set of servers (known as a pool) configured for images. If /video is in the URL, that traffic is routed to another pool optimized for videos.

Also see:
Options for Load Balancing Services in Azure
Azure Application Gateway - Highlights
What is the difference between Azure Application Gateway, Load Balancer, Front Door and Firewall?