I’m glad to read many people echoing (also my) very positive thoughts about the 70-300mm L. It’s a great lens on either APS-C or FF, and has a great feature set (USM, 4-stop IS, etc), fantastic IQ, solid L construction– and yet is really portable.
For travel, or as the OP stated, if one doesn’t like heavy (or long) lenses, then the 70-300mm L fits the bill so well. I have just taken it with me (and my wife) the other weekend for a day out, and I love this lens on my 7D… great for birds, portraits and just general photography outdoors.
I much prefer the 70-300mm L to the 70-200mm f/4 (as 200mm is too short for me, and the length of the f/4 lens is again, makes it not as portable).
The 100-400mm mkII certainly is also a great lens, and has that extra 100mm on the tele end, but it’s a completely different size (and shape). IQ between these 2 lenses is very very similar (you’d need to be a pixel peeper to notice the difference!) While I’d love my lens to be a 400mm (or even better 500mm or 600mm) – none of those lenses are ‘truly portable’ imho. For me, the 30mm difference on the wide end is important too.
Go with the 70-300mm L – I highly doubt you will be disappointed!
Paul