I assumed the top transmitter was the one to go for being nearest (1
mile away); that's the one which said "log periodic" aerial. But I
gather that's not the transmitter to go for then?!

Log periodics are used for transmitters that are located very close to the
receiving station. The advantages of them for this situation a

1. Very even frequency response means that a lower frequency high power
transmission (think analogue) won't overpower the weak low power
transmission which might happen to be at a higher frequency (think digital).
Log periodics are inherently wideband and suitable for digital transmissions
that may be far from the original analogue band of the site. They tend to be
more expensive and have lower gain than a conventional Yagi, though.

2. Very tight side and rear lobes help prevent the reflections and ghosting
that are characteristic of being in a high power area close to the
transmitter.

However, most of the aerials might use a high gain pointed at the far away
transmitter either because

1. the relay wasn't known about.
2. the relay is of exceptionally low power or is not line of sight
3. the relay doesn't support digital.
4. there is a large reflective object, such as a gasometer causing an
exceptionally hard ghost image from that relay which is easier solved by
pointing at Winter Hill than by fiddling about with stacked arrays.

Christian.