Websites don't have much that is "best" for all sites. There are different ways to serve mobile content and whichever way works best for your site is the "Best".

If your site is built on a handful of templates it may make sense to serve it all from the same set of templates. If pages are dynamically generated sometimes it can be too difficult to get all components functioning in harmony and two sites makes more sense. I have not seen any preferential treatment for one method over another.

Good answer.

What I have noticed is that complicated sites with very complex modules like Drupal would require 2 sites. While the template might be responsive, different layouts for ecommerce ect...are not always responsive, different frameworks and all.

If I use Worpress or Static HTML, one site would be fine.

What is better, one website that is responsive to all screen sizes or simply having 2 websites? One for mobile and one for desktop?

When it comes to RWD, one size does not fit all, but one template can adjust to fit all sizes. :)

One site, one RWD template.

The CMS you use or static really has nothing to do with responsive web design.

I've done a few sites now using a RWD built from from scratch, bootstap, and BootPress/Wordstrap (bootstrap versions on WordPress) and they all work about the same way. I tinkered with some other frameworks than bootstrap, they were often incomplete, more DIY, and don't have nearly as much support.

Based on your original question, I would suggest studying a multitude of RWD sites to fully understand what it does before you start. I would recommend studying actual RWD sites as well as a bunch of templates.

Once you fully understand what RWD and bootstrap are capable of doing, it will be clear you can easily replace your current site template with RWD and it will work well for all devices.

There may be some exceptions out there, but so far I've never needed to implement more than one page to cover all platforms.

YMMV

When you use a template which changes the layout depending on the device, some information which is not displayed by a mobile device may still be generated or even sent to the mobile browser. Having a site which is optimized for mobile browsing may therefore generate and load faster which can be an issue with slow networks and bandwidth limitations.

My preference is to go responsive, as there are so many different screen sizes on mobile today. Make one template that works on everything and you have less "tinkering" to do.

Great advice guys.

My conclusion is this:

Simple sites, RWD
Complex sites, 2 versions

When things get dirty in Drupal with a multitude of modules and extreme complexity with compatibility issues and dependencies...having a plain m.site.com would be best in addition to the full blown PC version.

A simple 5 page wordrpess site, Bootstrap and RWD

some information which is not displayed by a mobile device may still be generated or even sent to the mobile browser.

Unless your pages are enormous it's not too much of a problem as the bulk of the code is in JS and CSS files that download once and are cached.

Plus, really slow networks can be an issue in certain countries, so it depends on where your customers are whether you even deal with that.

FWIW, the first page that loads can easily tell the server which platform is being loaded and subsequent page loads can be optimized based on that knowledge.

some information which is not displayed by a mobile device may still be generated or even sent to the mobile browser

Sure, if you're using a badly designed template. Anything that can be done in a hand-rolled stylesheet can be done by a halfway decent CMS.

Generating information is not going to be an issue unless you're talking about dozens of extra database calls on an excruciatingly slow server. Sending unneeded information can be unkind to the user. Which means unkind to yourself if it makes potential customers turn around and leave your site before it's even finished loading. (See nearby thread about average page size. Ouch.)

One site (where ever possible).

If you have a large team of people/resources that will allow you to manage two sets of code and content then two sites is an option.

It does depend on the site though, what kind of information it contains, the interactions the users require.

The complexity of the site is a strange one. What is considered 'complex'? Lots of content? Multiple content types?

When things get dirty in Drupal with a multitude of modules and extreme complexity with compatibility issues and dependencies...having a plain m.site.com would be best in addition to the full blown PC version.

This is more of a reason to redevelop your Drupal instance rather than opt for a secondary site. If you've got extreme complexity and issues with dependencies then redevelop the entire thing and look responsive.