It kind of depends on what you want the post to do: inform or attract.
When you join a group, it's presumably because you agree with the aims or principles of the group or you are a member of the class that the group targets. This usually means that the other group members are broadly similar to you in interests and tastes and thus Groups are the better bet for attracting new people to your page. If you like what they like, the odds are they will like what you are offering on your page and your engagement rate will be higher.
However, as the quoted answer above indicate, promoting page posts is something akin to a scam in that all you are doing in most cases is making the post show up in the timeline longer/higher/more often/whatever. While this will have some positive effect on people who already like your page, it doesn't do quite as much to attract new people. Furthermore, going after friends of people who have liked your page is much less effective in terms of attracting new followers. What appeals to someone who is similar to you may not appeal to their circle of friends, their spouse, or their relatives. You will get some level of likes and maybe even a re-share but the odds on a friend of a friend being sufficiently interested in your page are significantly less as it's an indirect relationship.
Targeting the audience provides you with some ability to control who sees the post and you would think that would be highly effective in getting more likes but the reality is somewhat different and if you search around a bit for statistics on clickthrough rates after controlling for the targeted demographic the results are fairly bleak.
On the other hand, if the post is meant to inform your page followers of something specific, promoting it will have that effect and it may be worth the cost. Promoting a post to followers will get it in front of just those people and raise awareness of the post content to your existing targets. It doesn't necessarily help you grow a follower count but if you need people to take action, it can be a pretty effective tool.