Potentially, the blood test is more accurate than the field sobriety test. However, there are a number of things that can go wrong and do go wrong routinely in a blood test. That is why you need to have your own forensic toxicologist reanalyze the blood from their crime lab just to confirm the results.
According to HG.org, one of the things that could go wrong is fermentation. If blood sits in a vial for an extended period without sufficient sodium fluoride or other preservative and without being refrigerated, then by the time it gets to the lab, it will begin to deteriorate and produce alcohol within the blood. The blood is an organic substance, and when fermentation takes place, alcohol is produced.
The second is coagulation. If the blood is sitting in storage without anticoagulant, then the blood coagulates. As it does, solids form, leaving less liquid. It is the liquid part of the blood, the plasma, that is going to be analyzed. With less liquid, the amount of alcohol proportionately increases, and you are going to have a higher blood alcohol concentration.
Finally, the other thing that could go wrong is the chain of custody. They have got to prove that the blood they tested came from your client, and that is not to be taken for granted. These things could be misplaced or mislabeled between the time the police officer gets the blood and when it goes to the evidence locker. For example, if the blood is transported to the crime lab and is put in a batch of 40 vials, it can get mixed up.