Are smaller rear extensions more likely to be approved than large ones?

Not necessarily. There are several planning routes available, with varying chances of success:

  1. Apply under Permitted Development rights. A single-storey 3m-deep rear extension is allowed. Neighbours have no rights of objection
  2. Apply under Extended Permitted Development rights. A single-storey 8m-deep rear extension is allowed on a detached property; 6m on all other property types. Neighbours have objection rights; the planners can reject if there are valid planning reasons eg overbearing, overshadowing, sense of enclosure.
  3. Apply under a normal Householder planning application. This allows for any length or shape of extension. Neighbours have objection rights; the planners can reject if there are valid planning reasons

The critical issue is probably how well you get on with your neighbours, in particular those that share the immediate boundaries of your property with you. To some extent, it also depends on what existing garden walls, fences and structures exist to the rear of your property.