Unfortunately, there does not appear to be a strong consensus among vets on this topic; however, based on my research (largely including information about humans with type 1 diabetes), it seems the answer is:
Insulin injection site has an impact on the effectiveness, but it is far more important to pick a site and be consistent
The main reason that the injection site makes a difference is because different sites have different insulin absorption rates. 1,2 The absorption rate is determined by a number of factors, including capillary density, type of tissue at the site, amount of blood flow, etc. In humans, for example, injections in the stomach are absorbed faster that injections in the buttocks.
With dogs, the three primary injection sites people use are the shoulder, the thigh, and the neck. Of these, the neck has a slower absorption rate than the other two, which are generally the same. This means that the same dose injected into the neck will take longer to have an effect, but will also last longer (a slow absorption rate has an "extended release" effect).
(NOTE: It is strongly recommend that you do not inject into your dog's abdomen unless you check with your vet! That site is generally used by people that are prescribed rapid-onset insulin, while dogs are almost alwaye prescribed NPH insulin, like Novalin-N, which would go into the arms, legs, or buttocks.3. Humans also tend to have large fatty deposits in the abdomen, which your dog may or may not have.)
The primary impact of this for pet owners is that changing injection site changes how quickly the glucose level goes up and down. In my case, my vet does a weekly glucose check at the same time every week, so changing the injection site means the same dose at the same time in the morning would result in different readings. And, in fact, when I switched from thigh to neck, my dose did increase slightly, but the glucose also seemed to stabilize better.
In humans, it is common to pick different injection sites for the morning and evening dose -- a fast-acting injection site after breakfast, where you will be awake to monitor your glucose during the day, and a slow-acting site after dinner so it works all night. For pets, you will want to be more consistent, since your pet cannot readily warn you if something "feels wrong" until the problem gets bad enough to show physical symptoms. It will depend on your specific situation, how often you can check your pets levels, how well monitored they are, etc.
Ultimately, as with everything else, you should talk to your vet if you are concerned. Just be prepared to explain your concerns, as this is apparently not the kind of detail many vets are aware of. (It helped for me to show my vet the information for human diabetics.)
There are other factors that go into picking an injection site, so you should factor all of these in when making your decision:
- You should always rotate your injection sites, or you risk conditions like lipodystrophy (changes in the subcutaneous fat), which will make the injection less effective.4,5 Choose different sites in the same area, e.g. opposite shoulders, or opposite sides of the neck.
- Your pet may take better to certain sites than others. For example, the neck seems to be a preferred injection site for other subcutaneous injections (it's where your vet probably puts their vaccines) because it's the least discomfort. Picking a good injection site will not help if your pet's struggles make you miss the injection.