Since both options are available in Facebook, thought I'd do a quick post on them and what are the pros/cons of each. 

Option 1: Boost Post

Boost post allows admins to quickly promote a post from the post itself or from the Insights > Posts tab.

Option 2: Promoted Post

Requires ad managers to manually enter demographic targeting for posts. This obviously takes longer in setting up.

Here's a quick summary of what are the main differences and why Promoted Posts option is much better than Boost Posts.

Criterion

Boost Post

Promoted Post

How to find it?

Insights > Post tab

Ad Manager / Power Editor

Duration

Maximum 7 days

None

Ad Placement Control 

None

Desktop Newsfeed, Mobile Newsfeed and Right Column

Interest Targeting

None

Keywords can be chosen

Behavior Targeting 

None

Digital Activities, Mobile users and Travel

Connection Targeting

Fans and friends or demographic targeting used in posts

All users, People connected to page (or not), Friends of fans

Bidding Options

None

For engagement, Clicks or Impressions

Ad duplication for multiple posts

None

Ad details can be copied and used for multiple posts

Here's a longer version of the main stuff from above:

Ad placement control:

Having tested Right Column ads in Facebook, I think that paying for these would not be wise. It's almost as if users develop blindness to right column ads (on Facebook or other sites as well). If in doubt, you can always sort your post promotion data by placement to see check how your past promoted posts have performed (CPM, CPE etc).

By choosing Boost Post option, you lose control over where your post gets promoted. Under Promoted Post option, you can always decide if you want your promoted posts to appear on (desktop or mobile) Newsfeed and / or Right columns.

Interest / Behavior Targeting:

Interest Targeting allows ad managers to choose keywords that may be directly related to their brand. Behavior Targeting helps choose particular mobile OS, device manufacturers among other options (think promoting a post to competitors).

Connection Targeting:

This option lets Promoted Posts have a big upper hand on Boost Posts. The former allows users to create separate Ad Sets for friends, friends of fans, People not connected to the page, All and then monitor performance of each Ad Set (Also, because Ad Manager cannot separate ad data to show performance levels for such connections...Creating different Ad Sets is the only way out!). 

Boost Post has only 2 options: Promoting to all friends and fans OR using demographic targeting (applied in a post) to show ads to that audience.

Hope this post was helpful in understanding the difference between Boost Post and Promotion. Looking at the two options, Post Promotion is definitely the way to go for Ad Managers and allows for narrower targeting and detailed performance review.