Should I install this on my own site or a dedicated installation or subdomain?
ProjectHuddle will work on both your main agency website (youragency.com) or a subdomain/dedicated installation (projects.youragency.com). However, if you have either option, a dedicated WordPress installation is a better choice. Here's why:
The first is you likely (and should) have some heavy caching happening on your agency site. ProjectHuddle is a bit more dynamic - content can change by the second, so additional configuration is needed to work with caching plugins. It's totally possible to use ProjectHuddle with caching, but you'd need to add exclusions to get it working properly. ProjectHuddle sets its own transients for caching that clear when content is updated, so it really has an internal caching structure - caching plugins aren't really needed with the plugin.
You'll likely need to make sure you have some type of SMTP service to deliver emails, or they may end up in spam filters. Trying to install ProjectHuddle directly on your clients' site, for instance, would burden you with needing to worry about their server delivering the email.
You May Have Specific Cross-Domain Security Requirements
You may have or want some specific security settings on your agency site that could prevent ProjectHuddle from working cross-domain. For instance, many security plugins add headers to your site to prevent it from being iframed on other sites. If these headers are added, then ProjectHuddle can't function properly.
Loading ProjectHuddle on external sites can put some additional strain on your server. Each time the script loads in needs to check for permissions and login requirements. If you connect a high-traffic site to ProjectHuddle, then you agency's server may feel the extra load and slow down. Putting ProjectHuddle on a different installation will prevent this since they are isolated.
You can better control the look, feel, and functionality of your "client portal" as you set up ProjectHuddle for your clients.
Ease of configuration/setup
Setting up ProjectHuddle on a single, dedicated installation makes it much easier to configure/set up. And, once you set up and configure ProjectHuddle, you're good to go. No additional configuration is necessary to get it working on different types of sites is necessary, since everything is powered by your WordPress installation.