The biggest difference between the EOS 7D and the EOS 7D Mark II is the much more consistent autofocus system. As someone who has shot over 50,000 frames on each camera I can tell you that the difference is noticeable, especially when shooting in AI Servo AF mode. The way the original 7D tended to jitter back and forth is not near as big a problem with the 7D Mark II.¹

There's also a pretty good improvement in terms of low light/high ISO performance.

The low pass filter (anti-aliasing filter) on the 7D was a bit too strong. The 7D Mark II, in my opinion, strikes a better balance between absolute resolution and reducing the effects of moire.

The four areas where the 7D Mark II outclasses the 7D for sports and action (such as birding) are

• Autofocus performance (in terms of speed, consistency, and overall accuracy)
• More accurate exposure control with a color sensitive light meter
• Handling speed
• The flicker reduction feature Canon has included in several cameras since it was first introduced in the 7D Mark II in late 2014.

I shot with the 7D for 3+ years and the shot-to-shot inconsistency of the AF system was that camera's achilles heel. It was extremely frustrating to fire off a ten shot burst and get 3-4 well focused images, 3-4 slightly out of focus images (evenly divided between front and back focused), and a totally blurry flyer or two, even when the target was moving at a fairly constant speed and direction.

I've been using a 7D Mark II for about three years and the AF system is much closer to the world class AF system on my 5D Mark III (which is practically the same as the AF system in the 1D X) than any other APS-C camera I've ever used. There's still a small performance drop compared to the FF 5D Mark III, probably due to the narrower baseline of the narrower APS-C sized mirror and the semi-translucent spot in the middle that allows light through to the PDAF array, but it is nowhere near as wide a gap as there was between the 7D and the 5D3.

The 7D Mark II AF system has 65 AF points, all of them cross type. The 7D had 19 AF points, also all cross type. Both have a dual cross type center AF point sensitive to f/2.8. The 7D AF system is rated down to -0.5 EV, the 7D Mark II can AF down to -3 EV.

Another advantage is the 7D Mark II's 252 zone RGB+IR light meter that meters red, blue, green, and near infrared light independently compared to the 7D's 63 zone monochrome light meter. Not only is the metering more accurate, but the color sensitivity capability of the light meter is actually harnessed to assist in tracking moving subjects in AI Servo AF mode. This would be a significant advantage for shooting birds in flight. The two Digic 6 processors handle all of the data bandwidth that requires. The 7D has two Digic 4 processors under the hood.

The 7D Mark II also shoots at 10 fps compared to the 8 fps of the 7D and can shoot nearly twice as many raw files before the buffer starts slow down the camera (31 vs. 17) as the 7D could when released in 2009. With the 2012 firmware update the 7D could shoot about 24 frames before the buffer filled. With a fast card you can pretty much shoot to JPEG until the card is full or the battery is dead without being slowed down by the buffer of the 7D Mark II! The 7D stalled at about 130 jpegs.

In addition to the much better AF performance, metering, and faster handling, if you ever need to shoot under flickering artificial lights such as those found in gyms and sports stadiums, the "anti-flicker" feature is worth the price of the 7D Mark II! The camera syncs the shutter to release when flickering light sources at 100hz or 120hz (or their harmonics) are at their peak. It supposedly slows down the maximum frame rate just a hair, but I still get 9+ frames per second shooting at ISO 2500!

• Because the lights are at their peak when the shutter is released, depending on the particulars of the lighting in a specific venue I can actually shoot anywhere from 1/2 to 2/3 to one full stop faster and still get the same exposure levels I got previously when I set exposure based on the average intensity of the lights rather than their peak. In the same stadiums where I once shot at f/2.8 and 1/500 second, I can now shoot at 1/800 or even 1/1000 second at the same aperture and ISO. Many times this is the difference for what I shoot between freezing the action and having the feet/legs and arms/hands of the athlete blurry with their movement.
• By releasing the shutter when the lights are at their peak in the cycle, every image shot in a burst has the same brightness and color. This allows me to apply the same WB and exposure correction to the vast majority of the raw images in post processing. My workflow is no longer bottlenecked by the need to custom color-correct every image separately.
• The consistency between each frame also means jpeg images generated in-camera are also the same brightness and color and much more likely to be usable straight out of camera (when I set the correct exposure).
• With both raw images and jpegs, the entire frame has a consistent exposure level and color. Players on opposite sides of the frame wearing jerseys for the same team actually look like they are wearing the same color!

For further reading:

Please see the comment stream to this answer to Why isn't my Canon 70D autofocus accurate in manual zone AF mode with a 50mm f/1.8 lens?

Here's a direct comparison between the EOS 7D Mark II and the EOS 80D, which is superior to the 7D in pretty much every way.

This blog entry from Roger Cicala, the founder of lensrentals.com and generally recognized lens guru. Autofocus Reality Part 3B: Canon Cameras

This answer to Are full-frame cameras bad for sports photography?

¹ All cameras, even the best, do it to some extent. The question is exactly how much they do it and is that range of variation within what we consider acceptable or not.