The AVR 1650 is a better buy in my opinion as it has some added connectivity that is worth the extra $100.
From the Manufacturer
As the perfect A/V receiver for budget-conscious film lovers and audiophile who is looking for just a little bit more, the harman kardon® AVR 1650 has an impressive list of features designed to take your home entertainment to the next level. Thanks to HDMI v.1.4a with 3-D, Deep Color and Audio Return Channel, this versatile receiver brings a multidimensional TV viewing experience to your living room, offering all the latest Dolby TrueHD and DTS-HD Master Audio decoding technology and harman kardon Logic 7 processing, while creating an exhilarating 5.1-channel, 360-degree soundstage for your movies, TV shows and games. And with four HDMI inputs, extensive video and audio connectivity, and the ability to connect with a harman kardon The Bridge IIIP (available separately) for iPod/iPhone playback, the AVR 1650 gives you all the flexibility you need to configure a dream home theater system that truly blows people away.
- HDMI® v.1.4a with 3-D, Deep Color and Audio Return Channel
- Powers a 95-watt, 5.1-channel surround-sound system
- Dolby TrueHD and DTS-HD Master Audio™ decoding
- Logic 7 processing
- The Bridge IIIP connectivity
- EZSet/EQ™ equalization
- Four HDMI inputs
- Extensive video connectivity
- Extensive audio connectivity
- Color-coded binding post-speaker connectors
- On-screen display (OSD)
- Dot-matrix display and screen-saver function
- Multidevice, programmable remote control
- Headphone jack with HARMAN headphone surround mode
- Upgradeable firmware via USB port
- Detachable IEC power cord
Long story short, here are the added features from the AVR 1565(Again, you can check out the main features here on the AVR 1565):
- There is the obvious added HDMI port (AVR 1650 has 4 HDMI Ports)
- The added 25 Watts per channel giving the AVR 1650 5x95wpc
- ARC(Audio Return Channel)
- The AVR 1650 also supports the Optional Bridge IIIP iPod dock
- EzSet/EQ auto calibration microphone
If you're interested in other models?
-Harman Kardon AVR 1565
-Harman Kardon AVR 1650
-Harman Kardon AVR 2650
-Harman Kardon AVR 3650
AVR 1565 just for the above features which would give you some futureproofing that may prove useful even if you don't need the features today. For the $100 extra, go for it.