It's a combination of slow server/database and too many plugins/queries running.
Wordpress is more static in nature and can employ better caching mechanisms...
This is a bit off topic, but it's interesting, the WP installation with Google pagespeed shows TTFB / server response time:
<.20
www.site.com/index.php
.50
www.site.com
.70 site.com
.90 site.com/index.php
I wonder how to get it so they all hit <.20. The results were consistently different depending on which home address I used.
With the forum the results were much closer together @ .50-.60 regardless of home link.
So based on my debugging... It's likely due to too many plugins? It looks like about 85 queries on index page. I'm using cloudflare as well.
Okay... I figured out where the majority of the sql queries were coming from. It was a plugin. I turned off the plugin and ended up with 15 queries instead of 80+, but it made no difference in TTFB. Even after flushing cache with cloudflare.