This is always a tough question to answer. In most situations, it is better to refuse a breath or blood sample, and require the officer to get a warrant. I will go through some of the potential benefits of refusal below.
First, some smaller counties do not always have a judge or magistrate on call 24 hours to sign a blood warrant. In this case, if you refused the breath/ blood test, the officer would not be able to get a sample, and there would be no blood alcohol evidence in your case.
Second, the warrant itself can give rise to several issues in DWI cases. To get a search warrant, a police officer must provide a probable cause affidavit alleging the details of why he stopped you, any signs or clues of intoxication that lead him to believe you were driving while intoxicated, and that he believes by refusing the test you are attempting to hide evidence of intoxication. When the probable cause affidavit does not have the proper information, or if the search warrant is not executed correctly, an experienced DWI attorney can get the blood thrown out of evidence. Again, in this circumstance there would be no blood alcohol level in your case.
Also, there are more ways to get blood thrown out of evidence than there are for breath. To have a proper admissible breath test, fewer things have to happen and less people are usually involved in the process. Therefore, there is a lesser chance of human error.
In a breath test case, often there are only one or two officers involved with the stop, arrest and breath test process. Then there is a technical supervisor who makes sure the breath test machine is working properly.
In a blood case, you usually have the officer who stopped/arrested you, the judge who signs your warrant, the nurse who takes your blood, the officer who transports it to the lab, the person who receives the blood and stores it, and the analyst who prepares the sample and tests the blood. Thus, there is a greater chance of human error every step of the way.
There has been some debate amongst attorneys about breath versus blood. Some attorneys argue that when the breath or blood test cannot be thrown out, and will be coming into evidence, juries tend to distrust a breath sample more than a blood sample.
Either way, you want to hire an experienced DWI attorney who knows how to fight your case, regardless if there is a breath test, blood test, or no BAC in your case. You want an attorney who has the legal knowledge to get breath and blood results thrown out of evidence, and who can also successfully argue a case to a jury with the BAC in evidence.