In the past I have used the crossed arms style comfortably, it never hurt any part of my shoulders or neck. A few days ago I tryed the clean style and it hurt my wrist and shoulders more than anything but I did that style the whole workout anyway, I felt I was able to stay upright more than the arms crossed style.
My shoulders have been sore as hell to the touch right where the bar laid across for like 3 days. Is this normal, will my body adapt so I can front squat like that more frequently or did I have the bar lying across my shoulders the wrong way?
If somethings hurts, don't do it. Obviously you need to decide if its normal workout soreness or something more harmful. However, definitely check out the T-Nation youtube page. CT goes over in one of the videos exactly why he feels both methods you describe have negatives. CT recommends you use lifting straps to best protect your upper back as well as help the lift. This method still lays across the shoulders, however, so if you are experiencing pain from the bar there, maybe try padding. Personally, I had pain when I first started but am fine now.
Hopefully this helps you, since CT has been very busy and doesn't seem to check this forum. If you really want his advice, I suggest posting in his livespills.
I've found that one of my shoulder droops if I do cross style grip, so that's why I do clean grip. As mentioned above, lifting with straps is a good alternative. I tried it once and it seemed to make my keep my elbows higher (which is a good thing) as I couldn't use my fingers to stop the bar rolling down my arms.
my .02 is take a few times to get used to the Oly style- if you are way too stiff to conform to oly style abandon ship & use the strap method
an exercise that helped me was bottom up front squats from just beyond 1/2 depth - I really sucked at the oly position at first but can handle somepretty solid weight, most of my client over the years have been able to successfully adapt
i will add that oly style is best suited for low to mid reps, I've trained with a good # of olympic lifters over the years so I am probably a bit prejudiced, but something just feels sweet when u master it