From my understanding, you can rank either way. People talk about ranking within 7 days of getting their domain. 14 days is another average response I seem to get.

I really don't know if this truly plays a role or not. It seems like it is an issue that people debate about a lot.

I think age factors into the algorithm somewhat, especially if the older site has been at the top for a very long time. I've seen this happen with one of my sites.. my site has more original and optimized content, more backlinks, and less outlinks yet my competitor is seated firmly in the #1 position and has been there for several years.

Age does't means all means are quality seo and baclinks
This is my opinion

All things being equal, an aged domain would rank better.

However, as mentioned above, a little onpage and offpage SEO would allow either page to rank well.