Pure personal taste and tone goal. LG's sound like GREAT old mid 60's J basses. If that's the tone you dig, get one of those. It's again, not that they don't cut through, but rather that if you are looking for that grindy, bright top end of an ash/maple instrument like an LM, you just aren't going to get that with an alder/RW instrument. Just different things.
So again, I don't think anyone is saying the LG (or quite frankly, any bass) is not capable of sounding great on a gig or sitting in a mix. The LG does that beautifully.
However, an LG sounds like more like a 60's Fender, and an LM sounds more like a 70's Fender. Neither is going to really do what the other does, but both do what they do wonderfully.
I believe what Peter (and I) are saying is that, at home, solo, the LG seems to have quite a bit of pop up top. That's what can really disappear in a mix (it isn't what those basses are about). The LM can sound a bit over the top and harsh (as many ash/maple basses do) in a solo setting, but once you get them in the mix, that aggressive upper mid grind can actually still be heard.
So again.... just depends what you are looking for, not 'better or worse'. You will not be able to make one sound like the other (that's why I have and love both models), although you will have an easier time (IMO and IME) taming the LM than you will 'grinding up' the LG.