Vnc Viewer does not connecting but Windows Remote Desktop works

Yes. In Finder, use Command-K (or use the Go->Connect to Server...) menu command, and type

vnc://host:port

as the connection string. You will be prompted for a password, if necessary.

You're absolutely right in your observation that, typically, VNC requires more bandwidth than RDP.

VNC is a "bandwidth hog" because it's oriented at duplicating the pixels of the remote display. Conversely, RDP is based on drawing primitives (boxes, lines, etc) rather than sending pixel updates. Think of it like this: In VNC, the pixels on the display that change get sent over the wire (simplified somewhat). If lots of pixels get modified-- say in drawing a large box in the middle of the screen, a potentially large number of pixels are modified and need to be sent over the wire. In RDP, the instruction "draw a box in the middle of the screen" gets sent over the wire (which is much more concise than a list of pixels to change) and the client "draws the box". (I'm radically simplifying this and not considering VNC compression at all, but this gives you a general idea of how it works.)

You can use various "flavors" of VNC that have different compression options, but at the end of the day the RDP protocol (and protocols like it-- ICA, X, etc) are very difficult to "beat" because, fundamentally, they need to move less data to accomplish the same effect.