Objective The Mini‐Mental State Examination (MMSE) is one of the most frequently used cognitive measures for dementia severity and linked to deficits in everyday functioning. Recently, the Montreal Cognitive Assessment (MoCA) and the Addenbrooke's Cognitive Examination III (ACE‐III) increasingly substitute for the MMSE. However, there are no specific cutoffs in the ACE‐III for mild dementia. The objectives of this exploratory study were to assess the sensitivity of each scale to everyday functioning and to examine the cutoffs between mild and moderate dementia on the ACE‐III. Methods People with mild dementia completed the MMSE, MoCA and ACE‐III, whilst informal carers completed the Revised Interview for Deteriorations in Daily Living Activities for Dementia to rate their relative's initiative and performance of instrumental activities of daily living and the Katz activities of daily living scale. Data were analysed using correlation analysis, raw score comparisons, Cohen's kappa and receiver operating characteristics analysis. Results Thirty‐three dyads completed the measures. The ACE‐III was the most sensitive tool for everyday functioning performance, whilst its language subscale was specifically related to initiation of activities. The most suitable cutoff on the ACE‐III between mild and moderate dementia was 61. Conclusions Findings suggest the ACE‐III more efficiently identifies everyday functional impairments. Further research is required to confirm these exploratory analyses of the cutoff between mild and moderate dementia on the ACE‐III. Both functional impairment and stage of dementia are needed in the diagnostic process and in the clinical assessment of people with dementia. Copyright © 2016 John Wiley & Sons, Ltd.