Which kind of branch prediction is more important?
I don't know which case is prevalent, but I would like to offer some thoughts on your proposal of double pipelines.

First of all, you would need double the wire which would consume double the energy and produce double the heat while active. While not needed, on the other hand, it would be completely useless. So one could argue that it is not a good use of resources that are rare on modern processors.

More fundamentally, unless you prefer one branch based on probability, how do you know which version to write through? If none, you might not save anything because other processors might have to wait on your decision, anyways. If you stick with one of them, you have essentially the same rollback probability and cost as you have now.

Let us do a rough calculation. For sake of simplicity, let us assume that handling two pipelines instead of one does not cause additional management overhead. The expected cost (e.g. energy, heat) is $C = c + p(c_r + c)$ with one pipeline ($c$ the cost of executing either alternative, $p$ the probability for rollback and $c_r$ the cost for rollback without the cost for executing the other alternative) but either $2c$ or even $2c + pc_r$ -- either is a lot larger than $C$ if $p$ and $c_r$ are relatively small, and $p$ certainly is (as far as I know, modern branch predictions have accuracies over 90%). And we don't get much for this cost! Expected execution times are $t + p(t_r + t)$ with one pipeline and $t$ resp. $t + pt_r$ with two; as $p$ is small, time savings are negligible.