Heroku Postgre Crane DB vs Linode 1GB with Postgre installed

Heroku Postgre Crane DB vs Linode 1GB with Postgre installed

I'm trying to decide between using the Heroku Crane PostgreSQL database
($50/month - https://postgres.heroku.com/pricing) or setting up a Linode
1GB Ram / 8 CPU / 48GB Storage / 2TB Transfer instance with PostgreSQL
installed ($20/month - https://www.linode.com/).
I know that from a management perspective, using Heroku Crane Postgre
would be much easier, as everything is managed with security and backups
taken care of.
What I was curious about is how performance of the two databases would
compare. With the Linode 1GB / 8 CPU instance, only my database will be
used on it. I see with Heroku Crane that it says it only gets 400 MB RAM.
It also isn't clear with Heroku Crane how many CPU's I get and whether its
a dedicated instance.
Does the Heroku DB manages the RAM/Cache of the DB more efficiently? Its
unclear to me whether the Linode Postgre instance would automatically use
the 1GB RAM available to it efficiently, or if it would require custom
setup on my part to ensure the DB is loaded into RAM.
If it is that the Heroku DB would be less performant for the money, but is
a better deal because security, backups and management are taken care of,
that is probably acceptable, I just want to understand the tradeoffs.
Thanks for any info people can provide. I'm new to DB management, and have
been using a Linode 1GB instance with Postgre installed for development
and testing, but now that I'm going to production, am questioning whether
to move over to Heroku Crane. Also, not sure if this matters, but my
server is hosted through Heroku web instances.