I m both *G with TK and LH and recommend to take the same route.

With TK award availability is difficult (going to an office!) and being based in London, I find hardly any availability on flights ex London.
However for flights in Y or within Europe, you often earn more miles with M&S (MM will only credit 750/1250 in Europe compared to M&S crediting 100 % of the distance).
A big disadvantage is that M&S miles are only valid for 3 years...

LH has got excellent availability and earns 200 % (+50 % elite bonus) in J.(TK also earns 200 % but only on TK flights)

with programmes having their +/- and giving you 2 years to keep your status, I recommend to join both M&M and M&S.

You are can easily get and maintain *G with M&S and at least *S with M&M. (*S gives you lounge access with LH and the elite bonus)
Both status are valid for 2 years

Any miles you earn on top of the required 35K to maintain the status in each programme (every other year). you credit to the programme that gives you the most miles (or the lowest redemption).
If you reach the higher status (E+ or Senator) you have also a soft landing, making it even easier to maintain the status and credit your flights to the best programme