I like jungly gardens, with as much unmanaged and unmown area as possible.
However, I am fortunate in having, for the most part of my life, lived in properties where gardens are measured in acres rather than square feet, so there's plenty of space for all interests.
Meticulously tidy gardens I find singularly unattractive, but that's not to say that some parts of the garden - such as where the vegetables are grown - shouldn't be well cared for.
I like a garden that merges seamlessly with the surrounding countryside, but again I have been fortunate to have spent almost my entire life living in very rural areas, where such a thing is possible.
I do think that urban gardens, particularly in new-build developments, are a real problem. They cover a large proportion of our country, and could be such havens for wildlife, but on the whole they're pretty barren, having been mown and weeded to within an inch of their lives.
Rural gardens are already pretty good - even the fairly tidy ones - but anything that encourages urban dwellers to create a bit of space for wildlife in their gardens has got to be a good thing, and gets my full support.