In your opinion when working with older adults, what is more useful: strength-training, endurance-training, flexibility, balance-training, yoga, tai-chi...? You can add any others you may think of.
to date I haven't worked directly with older-adults but in my opinion strength training might have the greatest benefits.
Studies have shown that muscle strength is a good indicator of vulnerability and frailty as well as mortality after bone fractures in old age (i.e. Rantanen et al., 2002 - Muscle strength before and mortality after a bone fracture in older people). Additionally, strength and power training show hypertrophy even in old adults (i.e. Charette et al., 1991 - Muscle hypertrophy response to resistance training in older women) and a direct link to activities of daily living and independence (i.e. Rantanen et al., 2002 - Muscle strength as a predictor of onset of ADL dependence in people aged 75 years; Hazell et al., 2007 - Functional Benefit of Power Training for Older Adults; Hasegawa et al., 2008 - Threshold of lower body muscular strength necessary to perform ADL independently in community-dwelling older adults).
Furthermore, Hurley & Roth (2000 - Strength Training in the Elderly) point out that strength training for elderly people
- can increase endurance performance
- normalises blood pressure and reduces insulin resistance
- decreases both total and intra-abdominal fat while increasing resting metabolic rate in older men
- prevents the loss of BMD with age.
So for older adults, muscle strength might be a prerequisite for the other forms of physical exercise you mentioned.
That strength training improves cognitive and brain function and facilitates sensory processing (i.e. Wilke et al., 2020 - Free-Weight Resistance Exercise Is More Effective in Enhancing Inhibitory Control than Machine-Based Training: A Randomized, Controlled Trial; Chang et al., 2012 - Effect of Resistance-Exercise Training on Cognitive Function in Healthy Older Adults: A Review; Özkaya et al., 2005 - Effect of strength and endurance training on cognition in older people) seems to me like even more evidence to favor strength training for older adults.
I think that possibly a combination of several different types of exercise might work best and keep motivation and enjoyment at a higher level than one single type of exercise alone, but in my opinion, strength training should definitely be incorporated.
Asking to choose only one training modality as the best is similar to choosing between a spoon and a fork to eat. It depends on what you're eating--soup or steak. Likewise, training should focus on the individual's goals. I would submit that utilizing your choices in rotation would be more beneficial than choosing only one. Start with endurance to set a firm aerobic base, move to strength for ADL and postural/limb integrity, then on to agility/balance to optimize functional movement and minimize predisposition to falls/injury.
New research has shown that relatively intense short-term exercise combined with light aerobic exercise has a very good effect on the physiological performance of the elderly. This type of exercise is more effective in ensuring the physical and mental health of the elderly and their independence. In general, older people do not have much desire to perform relatively intense resistance training. In my opinion, an experienced physiologist would consider an energetic and effective combination exercise program when planning for the elderly. These exercises may include: a moderate aerobic program - relatively intense short-term intermittent exercises - resistance exercises that use most of the anti-gravity muscles - short-term stretching and flexibility exercises.
Multicomponent exercise programmes seem to be the ones with the most evidence when dealing with older adults, so a combination of all the ones you mention would probably be your best bet. However, if pushed to choose just one, particularly in frail patients, strength-training would probably be the one they reap more benefits from, the strength they gain consequently helping them maintain autonomy and improve their performance in the rest of modalities.