conorotc -- My experience is as a dad, and only with AROTC and VMI.
I think the answer depends on what you are asking. Are you asking about getting a 3 or 4 year national ROTC scholarship prior to entry? . . . or earning a ROTC scholarship once admitted and attending the school? . . . or participating in ROTC while at the school and earning a commission? . . . or are you asking if due to the competitive nature of gaining entry into one of the small SMCs does it hurt your chances in gaining an ROTC national scholarship?
Here is a link to the entering class profile for VMI Class of 2021:
http://www.vmi.edu/media/content-assets/documents/admissions/Profile2021.pdf
The entering class each year for VMI is around 500. For VMI, every cadet that enters VMI will be in an ROTC. For those not pursuing commissioning, they participate as part of the Army ROTC department.
Winning a 4 year AROTC scholarship is difficult. It recent time, AROTC offered approximately 2500 total scholarships each year with about 600 of those being 4 year and 1900 being 3 year. I think about 60 of the incoming freshmen to VMI showed up with either a 4 or 3 yr AROTC scholarship (this is my guess based on what I observed.) I don't have the numbers, but cadets do have the opportunity to earn ROTC scholarships after entry to VMI, and that is celebrated well by the school and the ROTC departments. Of the 500 that enter each year about 300-350 graduate (it looks like the class of 2018 will actually have closer to 400 graduating but that is unusual). Of the 300-350, about 50% (150-160) in recent years also commission.
As to whether the competitive nature of gaining entry into one of the small SMCs hurts your chances in gaining an ROTC national scholarship, I think it may only affect AROTC chances since you need to declare your schools as a part of the AROTC application. (Our experience with AFROTC was you won the scholarship first and then could take it to any school that had an AFROTC detachment provide you were admitted to that school. I'm not exactly sure how NROTC works.) My belief is that winning a 3 yr AROTC scholarship may be affected by choosing a small SMC, but I have no numbers to back that up, and it all may be a "wash" given the entry standards for most large non-SMC universities with large ROTC detachments (i.e., Notre Dame) or perhaps lower entry standards for smaller non-SMC universities and colleges with small ROTC detachments.