The illustrations have a huge role to play in this of course, and the way the Funny v 'Transporting' thing works in the visual field.
Funny deals in simple 'reduced to the essence' line drawings, in character and stance, details aren't important, as immersion in a created world is not in it's remit. Funny deals with the already familiar. Not necessarily familiar surroundings but familiar situations. Surroundings only ever need to be suggested.
'Transporting' deals in complexity and detail. Detail is important for believability, the more detail (up to a point) the more the possibility of successful immersion in the world created. I put books where the creation of a certain mood is important into this category. Funny doesn't really deal in mood creation.
The interesting thing about this split, to me, is the attitude of the public towards each camp. There is some of the time honoured (and unexamined) respect shown to work that betrays obvious evidence of hard work and 'skill'. But that is to be expected, unfortunately. Putting that aside, it does seem that work that speaks to perhaps a deeper place in their hearts and minds lingers longer in the public imagination than work which 'merely' amuses.
I have always thought that this was a bit sad, as a lifelong fan of Tom and Jerry, and The Beano, and books by people like James Marshall, I feel that they, and other work in the same vein will always be under rated in as far as bestowed 'greatness' goes. Probably because it deals with small, familiar situations and with humour, which is never considered all that 'important', or particularly hard to do. A bit like Picture Books ;-)
'Where The Wild Things Are', 'Winnie The Pooh', 'Peter Rabbit', 'The Tiger Who Came to Tea' 'The Snowman'. 'Tim All Alone' etc.
The interesting thing is that I can't as readily name a list of great funny picture books. I tend to think in terms of illustrators rather than in terms of actual titles. Artists such as Quentin Blake, James Marshall, Jon Klaasen, Tony Ross, Colin West, though much loved, would never top any 'best of all time' lists though they may come close. I think this is because once something is laughed at or with, it is perceived as being of lesser value than something 'serious', even if that perception is entirely unconscious.
Dr Suess may be the exception, but head to head with Sendak? There's a contest! ;-)