Effects of aerobic vs. resistance training on cognition The beneficial effects of exercise are well documented on cognitive ability (1, 2) and reducing cognitive decline (1). However, has the type of exercise ever been analysed?

In healthy adults, is there a difference on the effects of aerobic (running) and resistance training (lifting weights) on cognitive ability?
I tried to do a little research myself and like you observed, there is not much research being done on adults relating to this topic.

What I did find was research done by M.B. Pontifex et al. (2009). Although this research was done on healthy 21 year olds (Young Adults).

They researched the effects of aerobic exercise and resistance excercise on reaction time of tasks as well as accuracy of tasks amongst other things.

This data was collected via the following method:


  Twenty-one young adult participants completed a cardiorespiratory fitness test and maximal strength tests. On
  subsequent days, task performance measures of reaction time (RT) and accuracy were collected while participants completed a modified
  Sternberg working memory task before the start of, immediately after, and 30 min after an intervention consisting of 30 min of either
  resistance or aerobic exercise and a seated rest control.


Their observation was that after aerobic excercise their response time latency (reaction time) was decreased directly after or 30 minutes after the excercise. This was not observed after or 30 minutes after doing resistance excercise.

They stated:


  The current findings indicated shorter RT latency during
  a working memory task that was performed immediately
  and 30 min after an acute bout of aerobic exercise, relative
  to the pretest. Similar effects were not observed after acute
  resistance exercise or seated rest, indicating that different
  modes of exercise have differential effects on the executive
  control of working memory. Further, shorter RT latency
  was observed for task conditions requiring increased
  working memory capacity after aerobic exercise, relative
  to the pretest, providing support for the view that changes in
  cognitive function after acute exercise are disproportionately
  larger for tasks requiring greater amounts of executive
  control.


References:
M.B. Pontifex, C.H.Hillman, B. Fernhall, K.M. Thompson and T.A. Valentini (2009) The Effect of Acute Aerobic and Resistance
Exercise on Working Memory. Med. Sci. Sports Exerc 41(4):927–934