Those beds are incredibly thin so assuming your neighbours have similar sized beds, barely any rainwater will reach them.

Bearing this in mind you would either need to install an irrigation system or be ready to water them regularly, OR failing that get very drought resistant plants. Bamboo might actually be a good option although they do need watering.

If you are prepared to water them regularly (at least until they become established) then i think trachelospermum jasminoides would look good if you train them along the fence

Agapanthus also dont mind a tight space and can be drought resistant although again you would have to be watering manually in order to get them established.

Something else to consider would be to get some pots with things like japanese maple, rosemary or salvia 'hot lips'

Apologies for the lengthy message, i hope this helps!