DD was breech, and born at home with IMs. I was 31 at the time.
We found trying to track down accurate information on risk comparison very difficult. Part of the problem, as you've probably found, is that researchers and HCPs often don't differentiate between a medicalised vaginal breech delivery and a hands-off vaginal breech birth. They are very VERY different beasts (I wouldn't plan on the former if you payed me), with very different risk profiles. It can also be hard to get to actual, rather than perceived, risk - even when you talk to senior consultants.
Another part of the problem is that I couldn't find any published research comparing the outcomes of vaginal breech birth with either a breech delivery or a CS. A recent study done in Paris compared CS with breech delivery (with stringent criteria) and found breech delivery to be at least as safe as CS. Annecdotaly, talking to MWs with substantial experience in vaginal breech birth, this too can be a safe option. Pretty well everyone agrees that the safety of a vaginal breech, however its done, is strongly linked to the experience of your Obs / MW.
Two books I found very useful were "Breech Birth" by Benna Waites and "Breech Birth: What are my options" by Jane Evans. Plus anything you can find by Mary Cronk .
We were given some guidelines for what makes a good vaginal breech candidate - the baby should be normally developed and term, labour should start spontaneously (they wouldn't even offer me a sweep) and progress completely naturally. If any of those are not met then a CS is indicated. If those criteria are met, and if the MW is experienced in hands-off breech birth, then IIRC it is unheard of for a baby to be delivered up to the shoulders and the head to get stuck - either in the UK or throughout the international community. The reason I was given was that a normally develolped term baby's head is only marginally larger than its hips - so if the bum comes out, the head invariably follows. The head is known to get stuck where either the baby is premature, as then the head is dispraportionatly large, or when too much medical intervention is used (there's a theory that this can cause the cervix to start to close before the birth is complete).
In terms of which breech presentations are or are not safe, transverse is a non-starter and star-gazing (head tipped back) is strongly advised against (if the chin isn't tucked down well then it can get caught on your pelvis), but other than that they all tend to come out of their own accord or don't progress at all. The big risk is of cord prolapse - a frank breech is descending bum first and a bum is nearly as good a plug as a head so cord prolapse is pretty rare. As you go through full breech to footling breech so the chance of space between the presenting part and your pelvis increases, resulting in an increased risk of cord prolapse. I don't know what the risks actually are, but its still not that high. For what its worth, DD came out as a footling breech with just under an hour of pushing.
If you do want to persue a vaginal breech birth you may need to talk to the midwives directly, as consultants tend to recommend a CS or medicalised delivery (mine didn't even mention breech birth as an option). Ask for an appointment with the Head of Midwifery or the Senior Midwife - I'm not sure what the official term is. I'd be trying to find out whether they have breech skills in house and what their protocol is (and what actually happens) for diagnosed and undiagnosed breeches. If your PCT don't have breech skills and you're still interested, start calling IMs (they don't all have breech experience, but quite a few do) - I didn't book till 36 weeks in the end so its always worth a try.
At the end of the day, how you get your breech baby into the world will always be a very personal decision and there is no right answer. It doesn't matter what anyone else thinks as long as you are comfortable that the decision you make is the one that is right for you and your family.
Good luck, whatever route you take