300 f2.8 IS L II plus 2x Mk.III better than 100-400 f4.5/5.6 IS L?

I'd have loved to buy the 500 or even better a 600 f/4.0 II but it is for me too big for air cabin restrictions and too heavy to suit my travel needs - the 300 f/2.8 II is just a bit heavier then the 70-200 f/2.8 II L IS USM while still light enough and hand holdable for me and it is including the 2x III as good as the 600 f/4.0 (I) and only one stop slower - that's the kind of compromises I am happily willing to take on travel.

My travel photo equipment is just at 8 kg which fits Lufthansa's restrictions perfectly and it has no real optical limitations. (TS-E 17 & 90 plus 135 f/2.0 and STM 40 plus 300 f/2.8 and 1.4x and 2x plus 5D II plus lightweight rucksack)

As you said two different solutions - both have their merit

(with the 2x on a crop sensor plus the 300 II you would get a fabulous 960 mm FOV f/5.6 lens and not only a 640 mm FOV f/5.6 lens) and 320 mm more reach)

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