I think, as a metric of ability, STEP functions much better than BMO. Once you have covered A-Level Maths, all that stops you from bossing STEP I and II is practice. In the vast majority of cases learning new techniques will not be useful for STEP. On the other hand, although BMO1 in theory requires only GCSE Maths, unless you are ridiculously skilled you cannot get by just on prior knowledge. Even BMO1 success realistically requires knowledge of geometrical theorems, number theory and inequalities that you wouldn't come across unless you did a lot of specific study. As a result, BMO rewards people who have been trained specifically for it. I have no idea on the stats but I'd guess that if you looked at , say, the people who qualified for BMO2, probably the majority would have been training since year 9 or before. I'm not saying it's completely due to pushy parents, but I'd guess that it's often a factor.
The question then is whether they are useful with regards to each other. I'm not that good at either BMO or STEP, but I've used a bit of BMO number theory in STEP. That's probably about it in terms of technical maths.
However, BMO and STEP are both the only three hour exams most students will ever do prior to uni, and in terms of teaching mathematical perseverance and suchlike I reckon they probably help each other out a bit. Also, they are the only two exams that realistically test ability to prove things fairly rigorously. Overall, while the contents of the exams aren't much to do with each other, the style of the exams are somewhat similar, which I think could help a bit.