Welcome! From my very recent experience, the AutoCheck is MORE comprehensive when it comes to auctions or any other type of accident. If the car was ever sold at an auction, although that sale will show up on Carfax, the details may not be as comprehensive as they are on AutoCheck.
Carfax has let me down pretty hard in this regard and I would urge you to run both reports. The dealer should provide you with whatever service they use. CarFax is $60 I believe and AutoCheck is like $40 I think.
*Edit - My experience is with a different vehicle that I no longer have. Not my 50th which just hit 4k miles
. Thought I'd mention that