Thanks for that, the direct option does appeal. The key question that still leaves me undecided: is LHR-BKK-SYD in TG C better than LHR-FRA-BKK in LH C followed by BKK-SYD in BA C?
Are you buying separate tickets, or is this a thru ticket with only these choices? e.g. in a couple of months, I'm doing a BKK-SYD redemption, and I just need to get the LON-BKK sorted; in C, and sticking to star alliance, there are some better deals than TG/LH ex-LON: on LX (ok connection via ZRH, but they are retrofitting the A340s with flat beds, can use the TG codeshare ex-ZRH on the A346s, and you can leave from LCY), on OS (ridiculously easy connection at VIE, and fantastic food, but very slopey bed and No-VOD) and SK (ok connection at CPH). I am assuming you are ruling out MS and TK (which is not that cheap any more...)
Otherwise, the downside to LH is the nightmare that is FRA for non-Schengen connections; only the battered old 747s to BKK; not the most comfortable seat, and not the most charming service
For TG, you are fine on one of the newer retrofitted planes. I actually think the slope is one of the best for sleeping on, and the service will be better than LH - smaller cabin, so more intimate too. However, you have the problem of TG aircraft lottery - even on the flagship LHR route, something like 2% of flights are old aircraft, in which case, you may as well be flying Aeroflot
One upside to TG - there are 2 flights a day to LHR, and up to 3 to SYD, so connections are smooth, and if you are delayed, it's not such a long wait till the next flight