@karamazov I can speak only from the BA-only side (though with the benefit of a gap year), and the one thing I can is that it definitely depends from program-to-program, and also, from individual-to-individual. I completely understand why you're nervous. I was in a similar position last year, wondering how I'd compete those holding MAs.
I have seen that line of thinking floating around the forums and with some certainty, it does seem to be case. I believe there was one post that remarked that BA and MA applicants are either separated or are read with different lenses. As a BA-only applicant, it's fine if your project/research questions may need some ironing out (if there's one thing I've learned during graduate student recruitment, a program wants to also ensure that it leaves its mark on you). An MA applicant will most likely have the upper hand in terms of having a longer and more graduate palatable CV, but they've also had some years of experience in a graduate program already. Admissions committees (to my knowledge anyway) will be aware of what degrees you're bringing to the table and evaluate you accordingly. The one thing I can say for those applying with just BAs, I'd definitely make sure to try and point out your potential as a graduate student and make clear what kind of research trajectory you're on and how the department can help achieve your goals. A project and SoP (as well as a sterling WS) that is well-constructed, well thought out, exciting, makes an intervention/conversation within your field (and, I cannot stress enough, also one that the program can feasibly support) can and will catch an admissions committee's eyes, regardless if you're an undergraduate or graduate student.
I also want to stress that it also depends on what priorities and what kinds of students does the program desire (do they want those they can mold a bit more? have they had equal success with both BA and MA students? is one field over-crowded and one field underpopulated? etc.). Admission rates (from what I've seen from spending way too much time roaming through available admissions data), can be very elastic and unstable for some departments. Of course, this does not at all diminish the incredibly hyper-competitive nature of PhD admissions. However, the composition of what kind of cohort they want can absolutely change, especially from politics within and beyond the department (funding cuts leading to smaller cohorts to a department aggressively recruiting to justify more funding lines, which can cause an admission rate spike). That is to say, there's a lot of insider info/dynamics can influence a department's vision of what their ideal cohort may look like, so it is admittedly within the realm of the unknown.
To close off though, it is absolutely possible for BA-only applicants to be competitive in this tough environment. Cohorts are definitely mixed in with profiles of students who took varying and diverse paths to the program. I repeated this one mantra to myself when applying: present the absolute best version of myself as a literary scholar and leave no doubts to my capabilities, my potential as a graduate student, and my fit. After submission, it's out of my hands and it's up to the admissions committee to decide.