The closest thing I can find is this abstract Competitiveness in house and senate elections with identical constituencies | Political Behavior from the mid 80’s that states “When constituency factors are held constant, House incumbents perform slightly better at the polls than do Senate incumbents. However, the differences between House and Senate incumbents have not increased since 1920. On the contrary, the differences have narrowed somewhat.”
All it really says is even when the constituency is the same senate seats tend to be more competitive.
