I have more peace of mind with Big Dog because the company is still, or rather back, in business so that's one source of parts. Also (I say this having never wrenched on an AIH) it seems that most of the BDM components are not necessarily BDM fabricated, they use PM, Baker, stuff etc.
Turns out I actually do have a Harley now (friend was moving and had to get rid of it and offered it to me for half of book value) and there is certainly something to be said for the convenience of getting parts, bigger tank, not having to constantly polish it, etc. but even with full LEDs it doesn't get nearly, or any, of the attention the Big Dog does.
With that said IMHO the AIH bikes are the best looking of the three, or any brand for that matter
Beautiful set of bikes by the way