Hi Everyone
Thank you for all the interest shown in the study.
To answer a few of the questions and to respond to some of the comments:
About the author:
I am a sports physician and exercise physiologist.
I previously raced professionaly on the International MTB XC circuit, have 6 National XC titles and 1 National Marthon title. Was highest ranked South African rider on UCI rankings for 2003.
So yes, I do exercise and have experience of the specifics of the study.
I am also director of High Performance Cycling services at the Sports Science Institute of SA. We work daily with many of the World's best cyclists. Including winners of Grand Tours, World and National Champions.
With regards to PM's in general:
All of the athletes that we coach use Powermeters and we rely on them to optimise their training.
Does this mean that we prescribe all of our training on Power? 
No
From the study we conducted (more specifics about that in a moment) and from our own experience as well as that of other scientists (Lucia and Aldo Sassi are examples) we discovered that PM's are not the be all and end all as some proponents of Power would have everyone believe.
Firstly, we noted that despite the vociferous statements to that effect, there was not a single shred of scientific data to support the prescription of training by power. As a result, we decided to conduct our own study. We did not have preconceptions.
As you can see, for the specific interval session chosen, heart rate seems to be the better option.
This does not mean that HR is better for all training sessions. It may well be that for a Tempo session, T-max intervals and others, Power may be better. We simply do not know and until we find out, I suggest you toss a coin.
There are lots of problems with HR as outlined in our manuscript. Keeping readings stable in the field is just one of them.
There are also lots of problems with Power. Power zones change almost daily with fatigue and more long term with changes in training status. Lucia showed this quite succintly with his data from the Banesto team (including that of 5 x TDF champion Miguel Indurain). Power fluctuates by 50-100W over the course of the season whereas HR only 2-3bpm for the equivalent physiological intensity. To overcome this problem requires an aversive test such as a MAP or FTP test (both of which interfere with training).
So what should we do?
In our lab we look at both HR and Power. Rather than throwing either one out, we look at the relationship between Power and HR. This has led to the development of a submaximal test to evaluate not only training status but also fatigue (Lamberts submaximal cycling test). We have published a fair amount on this topic in recent years and are continuing to evaluate the methods to improve accuracy and reliability.
For now, PM's remain a terrific aid to coaching. They allow us to objectively quantify the requirements of the race scanario and to assess whether the rider is achieving the required workload both in racing and training. 
Coggan's TrainingPeaks software is a fantastic tool for the masses and allows athletes to analyse their performances, estimate fatigue and to look at all kinds of interesting metrics.
That said, training exclusively on Power is not proven and may not give you as great a training stimulus as training with HR.
Specific to the study:
We designed the study very carefully to ensure that the two groups performed identical training sessions with regards to mean loads. We then analysed the data to ensure that this was in fact the case. If you actually read the manuscript, you will see that we analysed ALL the training sessions and the mean HR and Power for intervals were identical between groups.
We speculated that the difference in the training stimulus was due to the very high power in the first 30s of the HR intervals, despite the much lower power in the second two thirds of the HR intervals in comparison to Power.
There is no evidence to show that holding a steady power is in any way advantageous. If you look at the optimal pacing strategy for events from the 4000m pursuit through to a 200km TT, none of them equate to a constant power. The most effective and common power profile is one which has a biphasic response (hard start, steady middle and surge at the end). Carl Foster and Jos De Koning have published extensively on this. Why anyone has come to the conclusion that you should go out and hold a steady power output in intervals and that this is beneficial is beyond my understanding. It goes against all the evidence.
With regards to the workload during the intervals. MAP is very much dependant on the method used to assess this. In our lab we use a 20W/min continuous ramp protocol, starting at 100W (it is the most common method used in the literature: 25W/min is also very common). Using this protocol, 80% is extremely tough to do 8 x 4min intervals (equates to just over 90% of MHR). So hard that some of the athletes in the group became overtrained despite only 2 sessions per week. The training status of the athletes was well above average and included many of the top provincial MTB and road riders.
We still use this session during the PreComp phase of training for many of our National team members. Most of them hate it because it is so hard.
With regards to the stats:
The method used (magnitude based inferences) is fairly new (contrary to one of the posts made) and was developed by Professor Will Hopkins (a bit of a stats guru). It is a very useful tool as it allows us to quantify the effect of the technique being used as opposed to trying to meet the null hypothesis. This is very useful in training studies and performance research as the margin between winning and being an also ran is often well below 1% (well below the ability of null hypothesis stats to detect). If you look at the studies conducted on:
Powercranks
Massage
Compression garments
etc.
None of the studies have been able to prove a benificial effect using null hypothesis stats yet athletes will tell you that the benefit is unequivocably there.
Finally, the only other study that has been conducted to assess the effects of training with HR or Power is still in review. It was conducted in the US and has no connection to our lab whatsoever. That said, I look forward to seeing the results being published soon.
I would implore those of you who have an interest in this topic to actually read the literature, think critically and not just shoot from the hip.
I am not going to respond to all the questions and the almost certain personal attacks that will come from Andy Coggan. 
I do look forward to reading the responses though.
Regards
Dr Jeroen Swart