There is a difference in being more competitive and more valuable. For some states (e.g, CA), there are obviously more people applying to a Senator than to any individual Rep. That said, Senators typically want to "balance" their slate across the state. So, even if hypothetically, the 10 "most qualified" candidates were all from the LA area, you can be sure that there will be nominees from other parts of the state, even if they are not as qualified.
Also, for some states where there is only one Rep (e.g., AK, WY), there is really no difference in competition. And, in some states, there may be fewer qualified candidates in the entire state than there are nomination slots meaning that certain districts in the country are actually MUCH more competitive than some entire states.
For the above reasons, Admissions doesn't care whether you have a Sen or Rep nomination in terms of how competitive you are. IOW, a Rep nominee from northern VA or parts of MD may be much more competitive than a Sen nominee from certain states.
As for how many on each slate are taken -- again, I know for a fact that some Rep slates have 8-10 of their nominees ultimately receive appointments and some Sen slates see only one. Even within a "competitive state," when the Senator "balances" his/her slate by taking candidates from different regions of the state, one of those candidates may well be "less qualified" than the #2 or even #10 candidate from a hyper-competitive district within that state. It is totally dependent on the quality of the applicant pool in each district and state -- across the board generalizations don't really hold.