Taking logs and testing the mean on the log scale would normally not correspond to a difference in means on the original scale.
[Edit: my comments apply to an earlier version of the data, and don't apply to the data that are presently in the question. As such, my comments really apply to the situation where the coefficient of variation in two close-to-lognormal samples are very similar, rather than to the case now at hand.]
The coefficient of variation is almost identical in the two samples, which does suggest that you might consider these as having a scale shift; if you think the logs look reasonably close to normal, then that would suggest lognormal distributions with common coefficient of variation. In that case a difference of means on the log-scale would actually indicate a scale-shift on the original scale (and hence that one of the means is a multiple of the other mean on the original scale).
That is, under an assumption of equal variance and normal distribution on the log-scale, a rejection of equality of means implies that the means on the original scale have a ratio that differs from 1.
It seems like that would be a reasonable assumption.
There are other things you could do, though.