I think we've covered it, but I'll summarise. The Level 3 BTEC is available in many 'sizes' - equivalent exactly in UCAS points as A Levels. If they're not academic to some degree then the chances of getting Distinctions is unlikely in every unit - some, like the dance ones are very practical and they spend most of their time dancing. If on the other hand, they're on the Performing Arts Business unit (NOT popular, but mandatory) then they need to be able to write, analyse, compare and contrast.
As for people looking down on them? Sure some people might, but you have to look at who these people are? Professional production companies, 18+ performing art schools and colleges certainly don't. For one reason. They KNOW BTEC very well - and can look at the individual units the kids have done, and what grades they got - and this is the real key - they can read the entire profile and build up an accurate picture of what they can do, not what they know? If you see somebody who is a 'merit' dancer but a 'distinction' arts admin person - you can be certain that they can do certain things. A distinction dancer in jazz, tap and musical theatre may be just what you want - the fact they got only a pass in business won't worry you. This is impossible with A levels - your weak areas are hidden completely.
Acceptance of BTEC at some unis is less good. However, those unis rarely are interested in performing arts. Those unis that do do performing arts actually like BTEC for exactly the same reason as employers and dedicated performing arts schools do. I have in my travels come across the complaint that BTEC wipes out 6 months of the 1st year of uni study, because they have to start with performance basics with the A Level people, because they know, but can't do!
To a large degree its simply that learning styles are the key. You can Google this if you are interested - but in essence people tend to learn best by one of three different types of teaching and learning. Watching, listening and doing. They have posh educationalist names like kinaesthetics - but this just means touchy-feely! Somebody who learns best by reading and going to lectures will not be happy with BTEC, because mainly it concentrates on doing. This is also why people who learn best by doing find A Levels really tough. Looking back at my own music and performing arts students over the years and facebook where we're all still in touch, you can see this confirmed by what they are doing. Those who are now in admin or pr style performing arts jobs were the reading and listening style students, who chose BTEC for the content, while the dance teachers, music teachers, drama teachers often now with an MA were the touchy-feely hands on kids.
Many did performing for just a few short years before getting much better paid jobs. I can probably name a very large number of my old lot who are now more qualified than I am who did BTEC. In fact, a rough count of schools and colleges with 30 miles of where I live shows far more music, dance and drama teachers with a BTEC education than A Levels. However, if there was a BTEC in being a doctor - it wouldn't work - wrong subject!
The BTEC system is, not quite so robust in schools at the moment. The recent government Wolf report identified the bottom end of Level 2 as being handled less well by school teachers used to GCSE. This is being rectified and will result in a new format for Level 2. Level 3 was untouched by the Wolf report.
Get your daughter to do one of the free internet learning styles tests - but look hard at the options on the questions, because these show you what other people could be selecting - you'll see clearly from the questions how differently people learn. These tests are pretty accurate, and usually, you cannot understand how other people could even consider the other choices.
She needs to make the best choice for her - not you, and certainly not us. She's likely to be similar to you, but if you discover she has a very different test result, then it's really unfair to inflict your choice on her because if she is kinaesthetic and you are not - then you learn differently. Drop out rate is directly linked to learning styles and suitability for a particular course. After a week or two colleges and unis can predict from observation, who is at risk of dropping out. This is why they very often then suggest a change of course.
There's a handy test here
http://www.open2.net/survey/learningstyles/ . It doesn't actually state what you are, as most do, but displays your different results in a graph, so if two people do it, you can compare. It doesn't produce results but lets you see how people are different, and why advice to others on the BTEC A Level issue frequently gets so difficult - because if you enjoyed your A Levels and did well, it's very odd to work out why somebody would be better on a BTEC course.
Sorry for the long winded reply. I'm stuck in a hotel in London, where we are writing a NEW BTEC for Level 2 Performing Arts, especially aimed at 14+ (because the current one is really suited to slightly older kids). Level 3 is not being changed - even though many schools and colleges don't seem to have grasped that the old National Diploma is now called the Extended Diploma because it's worth more UCAS points - it's best to check this is what is on offer, a National Diploma currently = 2 A Levels, and Extended Diploma = 3 A Levels. Nothing changed apart from the name.