I think I remember having more trouble doing everything in 2 with the time limit then I did in 1. I don't remember the details but I recall running out of time before and during the fight with the twins in 2 in a couple of runs. The worst I remember happening in 1 is having to bring some survivors with me to confront the cult and then lead a full posse through paradise plaza at night.Yeah I was going to say 2 wasn't bad but Applejack beat me to it. Actually 2 is probably more playable gameplay-wise. Never played Dead Rising 1 before but I heard the time limit was so severe and A.I. was bad.
1 gives you a few opportunities of calm to explore and learn where things are in between throwing lots of missions at you. I'd also say it has easier to find unmarked survivors.