Power meters are really useful for a few things:
#1 - adding a level of precision to training that heart rate cannot give you. Especially for short intervals, HR responds too slowly.
#2 - benchmarking against others and yourself over time and over varying conditions (flat/hilly, windy/calm, different bikes, etc.).
#3 - learning how to pace yourself - a PM will show you really quickly how much your output varies in a ride, and how you might be "burning matches" where you did not intend to.
There's a reason virtually every pro today trains with power - if you are serious about performance, you can't beat it.

For a leisure cyclist, while you would get something out of a PM, there are probably other places for bigger gains. From what I've seen (and I used to run a high end bike studio, so I've worked with many cyclists) most recreational riders need to:

• get a really good bike fit
• hire a good coach for at least 3-6 months to teach you the basics (including strength training and nutrition)
• invest in better accessories: shoes and bib shorts being most important

One other thought - Strava has a power estimator that might give you a taste of power metering, at least in the post ride analysis, I think it's included in their free service but you might have to pay for the premium to try it out.

Hope this helps!