I took nearly 2000 images on Sunday with my pair of 7Ds, most with 70-200/4 IS on one and 300/4 IS on the other. So far I've edited about 1000 of those images and have found a total of four where I missed focus. Emphasis on "I"... because of those four I am certain that two were my error, not the camera's. The other two, I'm not certain. This was mostly with moving subjects (an equestrian event... a hunter-jumper show). Now, I use Single Point, manually selected... and most often the center point. I often have to respond very rapidly and the 7D usually locks on instantaneously in good light, with these lenses. However I have seen the camera struggle a little in low contrast, lower light. There the 1D might be a little better.
I don't have a 1D series for direct comparison, have only used them occasionally and several times have hired second shooters who used them (who didn't seem to get any more or less shots in focus than me).
7D has nineteen AF points, all of which are dual-axis type. This may be a scaled down version of the AF system used in the 1D3 and earlier 1D series cameras, which have 45 points, nineteen of which are dual-axis type and 26 of which are the less sensitive single-axis type. So, while 7D has fewer points overall, they both have the same number of the more sensitive, dual-axis type. The 7D also uses a discrete chip to handle AF functions, similar to the 1D models (along with dual image processors to allow for a high frame rate, also similar to 1D series). AFAIK, the 7D is the only non-1D series model to have both these features.
Now, the 1D4 in particular saw an increase in dual-axis sensors, up to 36 out of the total of 45 (with f2.8 lenses and when selected manually.... reduced back down to 19 when auto selection is used or with f4 lenses).
But IMO, in many respects the 7D is a "1D series Lite".
There are some differences in the multi-point patterns you can set up on the 1D series, vs the patterns on the 7D. Both 1D4 and 7D offer Expansion Points (but remember that 1D4 can do it with more points). 7D also has Zone Focus, which 1D4 doesn't. With Expansion Points, focus always starts with a single, primary point... Then the surrounding points can take over if needed. The 1D4 has a couple forms of this. 7D only has one. Zone Focus is different because any of the points in the zone can serve as a starting point for focusing, then focusing can move to any of the others in the zone. It's sort of like All Points/Auto Selection, except it's limited to a particular Zone within the viewfinder. So, while similar, Zone Focus and Expansion Points act a bit differently.
7D has Spot Focus (Precision Focus), which 1D4 doesn't. Now, the AF points are a bit smaller on the 1D4 anyway, so this might not be all that big a deal out in the real world. On 7D, Spot Focus actually makes the AF point smaller, so that one can more precisely place the focus, handy for situations such as shooting through the branches of a tree or through a fence. Spot Focus on 7D is a bit slower than standard Single Point, so Canon doesn't recommend it for moving subjects. But I've seen people use it successfully with butterflies, which are pretty darned quick!
Via Custom Functions 1D4 can be limited to manually selecting 19, 11, 9 inner or 9 outer AF points. You can't limit 7D's manually selected points... it's all 19, all the time.
The 1D series also offer Spot Metering linked to the active AF point (limited to a somewhat reduced number of AF points... only 11 on many, but up to 19 on the 1D4). So, in other words, you can have off-center Spot Metering with the 1D series, which you cannot with 7D. I found this feature handy sometimes on my old EOS-3 and miss it a bit on all the DSLRs I've been using. However, I've learned to use Evaluative well. That isn't Spot Metering, but is similar in that it does place extra emphasis on the area right around the active AF point.
The 1D cameras are really nice. But I prefer the 1.6X crop. There is the perception of "more reach" with the smaller crop sensor... And in truth the 18MP 7D "puts more pixels on target" than the 16MP 1D4 (though it's not a huge difference), which at least psychologically allows using somewhat smaller, less expensive lenses... a 300/2.8 instead of a 400/2.8, or a 500/4 instead of a 600/4, for example. There is plenty of resolution in either case, though.
7D can fully use both EF and EF-S lenses (as well as third party "crop only" and full frame). The APS-H 1D series cannot use EF-S lenses and might see vignetting issues with third party "crop only".
I also prefer a removeable battery grip. I can reduce the size and weight of the camera for carrying, if I wish.
But really, either camera would be great. I know plenty of folks happily using each of them. Including some who are birders.
I would note that the 1D4 is a discontinued model now, and the 7D is likely to be replaced within the next 6 months or so (just a guess). It might be worth waiting.... or buy a used 7D now and plan a possible upgrade fairly soon.