I will get the ball rolling...but don't consider this to be the gospel by any means. This is my basic understanding. I am sure others can add to this, and possibly even correct me where I might be wrong or misinformed.
Consider the two common sources for bradycardia: cardiac and non-cardiac.
Peds tend to brady down due to hypoxia (non-cardiac) more rapidly and more profoundly due to underdeveloped sympathetic nervous system, allowing parasympathetic response to predominate.
Chemoceptors in the carotid and aortic body will detect low oxygen partial pressures (among other things) and depolarize, causing a release of multiple neurotransmitters, ultimately causing vagus stimulation, by an indirect pathway (i.e. not direct stimulation like laryngoscopy of deep suction.)
The bradycardia in peds is actually theorized to be protective in nature, and it is an initiation of a more developed mammalian diving reflex, which is ultimately diminished as we reach adulthood. This is why cold ice to the face and breath holding for SVT is more effective in peds than adults (peds have higher incidence of conversion due to vagal stimulation.)
Treating this bradycardia with atropine is counter-productive, because you are simply removing a protective mechanism, and not increasing core oxygenation in any appreciable way. I am not going to say epinephrine is your saving grace either, but adjunctively, while you take measures to increase oxygenation and ventilation, using epinephrine to shunt blood to the core can help reduce activation of these chemoceptors, which seems to be more effective than simply blocking parasympathetic response all together.
In adults, when presented with hypoxia similar to the description above, they respond with a sympathetic (fight or flight) response initially, which the pediatric patients typically can not do, because of an underdeveloped sympathetic nervous system. This will show the classic increased heart rate during initial hypoxia we are so used to seeing in adults, which is lacking in peds. Ultimately, the adult heart rate will fall though (through the same mechanisms), which is why oxygenation and ventilation are still key strategies in eliminating bradycardia in any patient who has hypoxia as the primary etiology.
This is not the common primary etiology of bradycardia in adults however. We all know that bradycardia in adults is more likely a result of cardiac ischemia, which has nothing to do with adequate oxygenation per se, rather, it is failure to adequately deliver well oxygenated blood to the proper areas (due to blockage.) We will see tachycardia in these cases initially also, however, parasympathetic activation will ultimately take place in an effort to slow down rate and decrease cardiac workload.
We use atropine because it increases heart rate more passively, through parasympathetic blocking, allowing sympathetic response to predominate. Epinephrine administration in this care can allow the sympathetic response to compete with the parasympathetic response triggered by the body, but at the expense of vasoconstriction.
Ultimately, my opinion anyway, is that it is always a choice between the lesser of two evils, as the REAL treatment is fix the etiology of the bradycardia, which neither of these treatments do. Epinephrine buys you time while to work airway, and atropine buys you time while you work cardiac circulation.
Remember, the current evidence recommends atropine first line for bradycardia in peds if there is known or highly suspected direct vagal stimulation as the source of the bradycardia. For example, if a pediatric patient bradys down after deep suctioning, and fails to recover despite oxygenation, it is perfectly ok to use atropine first, as this is a direct result of hypersensitive vagal response.
Lastly, the research indicates that not administering atropine and moving directly to TCP with or without inotropes is perfectly acceptable in a known high degree heart block. In fact, this is most likely best practice.
My best advice is that the order of events in the AHA algorithms are considered best practice for the most common presentations we see from patients. They are not meant to be sufficient for all situations, and the true best practice is to treat every patient based on their specific presentation and etiology, whether they be adult, pedi, or otherwise. This might mean that some peds get atropine first, and some adults get epi first, or go straight to pacing. I know most paramedics don't generally get to make these decisions, but physicians deviate from AHA algorithms all the time (sometimes intentionally, sometimes because they just don't know any better!)