Experience: 1 PBP and 1 LEL plus probably only 20 audaxes over 200km.
Aero: 2/10 (sure it'll make it easier but if you rely on being aero to get around audaxes in time then there's something wrong, plus aerobars are banned on PBP)
Structured Training: 2/10 (there was no structure to my training, I commuted and did other audaxes, again, it'll certainly make it easier but it's far from necessary)
Time on the Saddle and Recovery: 9/10
Physical Pain: 2/10 (if you're in proper pain then something isn't right, but expect plenty of discomfort)
Mental strength: 9/10 (giving up is easy, as you'll possibly find out as you do rides > 200km, pushing through is harder)
I'll add:-
Self-sufficiency: 7/10 (being able to fix things out in the sticks, including being inventive [I recently fixed a lost mudguard screw with some long grass from the roadside as nothing else would fit]. Being happy with this gives me confidence and stops me wasting time worrying about what could go wrong.)
Experience in different conditions: 8/10 (it's not all sunshine and daylight as it may be on 200kms, finishing one day at 2am drenched and getting a few hours sleep in a cot bed in a sports hall with 300 other snoring/farting riders, getting up and setting off again in the pouring rain, etc)
Suitable kit: 5/10 (far less important than physical fitness but having adaptable clothing [i.e. layers, etc] helps greatly)
The more time on the bike you have in the run up to the event (i.e. what you could call training) the better prepared you'll be, both physically and mentally. You'll suffer less discomfort (hopefully) and have more experience of night riding, riding solo for long periods, how your body reacts to heat/cold/wet/tiredness/fatigue/etc, how to feed yourself (what works and what your body really doesn't want at 2am).
One last thing, I gave up about 180km into a 600km ride, found a B&B and then got the train home the next day. Looking back it was probably the correct thing to do, but only because the weather the next day was horrendous and I probably wasn't experienced enough for it. But giving up that once means I *NEVER* want to give up again on a ride unless I absolutely have to. The shit patch(es) will pass, if you feel like giving up then get to the next control, eat something and then reassess. 99% of the time you'll feel fine to carry on.