What are the benefits of "powering up" vs leaving your Steem as just that...steem?

It's a trade-off between voting weight and liquidity.

Powering up converts your Steem to Steem Power. Steem Power allows you to participate in the reward pool voting, the process by which new author rewards are allocated between Steem users. The higher your Steem Power, the larger your influence on the reward pool voting (i.e. the higher your Steem Power the large your vote). Liquid Steem (non-powered up Steem) does not give you any participation in the reward pool voting.

However Steem Power is locked-in and thus illiquid. It takes 13 weekly instalments to power down (under the current Hard Fork 19) which means it will take 3 months to release all your Steem Power back to Liquid Steem. If you are looking to trade or cash-in your Steem then you need to bear in mind this locked-in period.

Powering up your Steem also has additional benefits:

• With more Steem Power you get a bit more attention on Steemit - it helps you rise above the mass of small accounts.
• Once you pass around 500SP you have enough voting weight to start splitting your votes (using the slider) so you can reward more than 10 people a day.
• Your curation rewards are increased since they are related to your voting weight.
• You get enough bandwidth to post frequently (this can be an issue with low SP levels).
• You can delegate Steem Power to projects that you like and still retain enough SP to operate (delegating SP is safer than transferring Steem or SBD to projects since you can always reverse the delegation - with a one week delay for it to be returned).