Is a more specific breathing technique better than just slow, deep breathing for calming oneself? We're told by a Big Think Mind Hack video (carried by some tabloids) that 1:2 inhale:exhale breathing technique is better than just slow, deep breathing for calming yourself. Is there systematic empirical evidence that one technique of slow/deep breathing (this 1:2 one or another) is superior to just less specific ways of slow/deep breathing for dealing with panic attacks or lesser versions thereof or more generally calming oneself?
Any anxiety — and especially with Panic Attacks — can often but not always lead to Hyperventilation.  Steady, slow breathing will prevent it, whilst also helping to relieve the anxiety.

Whilst looking into the answer to your question, there are a few resources out there discussing the best techniques for dealing with hyperventilation.

MedlinePlus.gov mentions that hyperventilation creates a low level of carbon dioxide in your blood.

The low levels of Carbon Dioxide is the basis of the paper bag technique which you may have heard about.

It is the traditional practice to treat acute hyperventilation (thought to be due to anxiety) by having patients rebreathe the carbon dioxide using a brown paper bag.  However, there are reports that there are cases in which this treatment, incorrectly applied to patients who were hypoxemic or had myocardial ischemia, resulted in death. (Callaham, 1989)

This will be the reason why WebMD states, although the technique is useful, that you must not use a paper bag if:


  You have any heart or lung problems, such as coronary artery disease, asthma, chronic obstructive pulmonary disease (COPD, emphysema), or a history of deep vein thrombosis, stroke, or pulmonary embolism.


or if you are at a high altitude [above 6000 ft (1829 m)].

Interestingly, MedlinePlus states in the same article linked above that the heart or lung problems mentioned by WebMD can be medical causes of hyperventilation and


  Emotional causes include:
  
  
  Anxiety and nervousness
  Panic attack
  Situations where there is a psychological advantage in having a sudden, dramatic illness (for example, somatization disorder)
  Stress
  


WebMD in another article states that breathing exercises help to deal with hyperventilation and suggests to


  
  Breathe through pursed lips, as if you are whistling, or pinch one nostril and breathe through your nose. It is harder to hyperventilate when you breathe through your nose or pursed lips, because you can't move as much air.
  Slow your breathing to 1 breath every 5 seconds, or slow enough that symptoms gradually go away.
  


MedlinePlus.gov also has a detailed explanation of Pursed Lip Breathing.

As for studies on effective long term treatments, Alicia Meuret of Southern Methodist University in Dallas led a study pitting Cognitive Therapy against CART (Capnometry-Assisted Respiratory Training).  After some searching, I found the Meuret's manuscript on the National Institutes of Health website (Meuret, et al. 2010)

Apparently, according to the LiveScience article linked above, Meuret said,


  Panicking people are often told to calm down and "take a deep breath," Meuret said. But for someone hyperventilating during a panic attack, deep breathing is a bad idea. That's because hyperventilation happens when people breathe so quickly and deeply that they expel an unusually high amount of carbon dioxide, which in turn causes symptoms like dizziness and numbness. Those symptoms tend to make people feel like they're suffocating, so they breathe quicker and deeper, further exacerbating the problem.


CART, was developed to systematically change hypocapnia in patients with Panic Disorder through a brief, tightly controlled 4-week training program that uses immediate feedback via a portable capnometer.  Here is a video showing the capnometer in use.

References

Callaham, M. (1989) Hypoxic hazards of traditional paper bag rebreathing in hyperventilating patients Annals of Emergency Medicine 18(6): pp. 622—628
PMID: 2499228 DOI: 10.1016/S0196-0644(89)80515-3

Meuret, A. E., Rosenfield, D., Seidel, A., Bhaskara, L. and Hofmann, S. G. (2010) Respiratory and Cognitive Mediators of Treatment Change in Panic Disorder: Evidence for Intervention Specificity Journal of Consulting and Clinical Psychology, 78(5): pp. 691—704
PMCID: PMC3327286 DOI: 10.1037/a0019552