Thanks - that helps me understand the question. What follows below is a discussion of just the technical issues, which I hope is helpful. Direct personal experience is going to be more significant - so give it a try and report your results, and we'll all benefit. :^)
The 6BL7 and 6BX7 are rated for 12 watts total dissipation, but up to 10 watts on one triode as long as the total is 12 watts. So for amps that need more than 6 watts dissipation per channel, you would need two in parallel. Crack only dissipates about 2.3 watts per triode so that is not an issue, though it may be with other amps.
The other thing that paralleling two triodes does is double the transconductance (which cuts the source impedance feeding the phones in half). The 6080 has the same transconductance per triode as the 6BL7, but the 5998 has nearly twice the 6080 transconductance. So a paralleled 6BL7 is roughly equivalent to a 5998 in that parameter. I suspect that is the main reason for the audible difference.
There are also (moderate) sonic negatives associated with paralleled triodes, at least to some people, so a good 5998 might be expected to have the edge - but they are expensive, hard to find, and the selection has been picked over for many years. You pays your money and you takes your choice.