Depends on the PBA pattern and the house pattern. As of today, I average higher on Viper than I do even a fresh house shot, much less an old one. But I barely average 150 on Cheetah.
If you'd bowled where I did from 1991-1996 and again from 1999-2001 (Leland Lanes, Tuscaloosa, Ala.), you'd say house shot was harder, too. That's because Leland used to put down a flat-earth, 12-units-across-all-boards shot and the all-men's average there was 30-plus pins lower than at the house across town.
Because "house pattern" can mean anything from automatic strikes down to a pattern put down by someone who either doesn't know or doesn't care how to lay one, it's hard to say. Once you break down a PBA pattern far enough, and once you break down a house pattern far enough, you pretty much clear all the oil out of the preferred track area and then they're equal.
On average, the PBA patterns will still be tougher. But it's not universal and in my personal experience, all the PBA patterns except Cheetah are far easier than a flat sport shot.
Jess