Improve existing startup ideas that have been done or think of something unique?

Is it better to improve a product or service that exists already or to come up with a brand new unique idea that isn't being done yet?

Building a company based on an incremental improvement usually puts you at a disadvantage for a couple of key reasons:

1. The leading player in the space can build your improvement more easily than you can catch up to their foundation.
2. Switching costs usually make it not worth your competitor's customers' time to use a different provider.

That doesn't mean you have to start with a completely unique idea -- those are exceptionally rare. But rather than thinking of ways to improve old ideas, think of ways to use old ideas in new ways. Most new companies take existing business models and apply them to new markets (e.g. all the 'sharing economy' startups poppingup now), or make different trade-offs to serve people in a market with different priorities (e.g. Mac vs PC).

I'd recommend reading Blue Ocean Strategy; their strategy canvas framework is a great way to visualize what leading players in the market have chosen to prioritize, and see where there might be space for a new entrant to differentiate.

This question is too broad, the answer depends on too many factors. The answer in the comment "Better as in one with the most likelihood to succeed." is already a wrong way to think about this.

IDEAS ARE WORTHLESS, execution is everything.

Very few successful companies reached product/market fit on their original idea - most pivoted a lot before they got the product right. Some pivoted away from original ideas 180 degrees. Read this great post by Steve Blank on pivoting unicorns.

Very original ideas can be much harder to sell to consumers than an improvement to something they are already familiar with. Unique doesn't always mean large market, it could be only a small group of people who appreciate the unique aspect. Of course there are some great examples like Twitter where original idea became a huge success. But look at Pinterest - they took a concept of a social network and changed it slightly - growth spike unlike any other social network. Here is another chart showing Pinterest growth against other networks.

Comparing the probable success between a fresh idea (if such a thing exists) versus a variation on a theme, is confusing cause and effect.

The one which will most likely succeed is that one that people will use, has a business model, can be executed by you, and has a good deal of luck involved.

Don't get me wrong, there are advantages to picking up where someone else has left off, or filling in missed opportunities - but there are equal amounts of disadvantages.