Do companies which offer template websites (such as Wix and Weebly) offer as much SEO customization and versatility such that they can not be considered less effective in Search Engine Listings, than building a website from scratch?
It all depends on the templates. There is no reason that a template site can't have good SEO. The template would just have to be designed for it.
You also may want to pay attention to vendor lock in. If you create a great template site and it starts to get lots of traffic, could you migrate it away from the template site if you wanted to? Can you give it its own domain name? Can you export your content? What happens to your site if the template company goes under?
Here is how the two you mention address SEO:
Wix websites appear to be single page applications with content all loaded by AJAX. They use
#!in the URL to implement the now deprecated crawlable AJAX standard. Google still crawls such websites, but it is unknown how long Google will support the deprecated standard.
Weebly example sites look better for SEO off the bat to me. The URLs look static and crawlable without using AJAX. It also appears that some of them have their own domain name.
Weebly also pays attention to SEO and has written articles about improving SEO for a Weebly site.
In the end you have more control if you build a website from scratch. On the other hand, a template website is a lot easier to get up and running. Much of SEO is getting content out there. If the template helps you get moving faster it may be well worth it to you.
I would caution about using Wix - they use Ajax URLs which have a the hash bang in the url (eg. www.abc.com/#!turtles ) which means that when you outgrow Wix, you can never do a true 301 redirect from those ajax URLs to a typical URL ( eg www.abc.com/turtles ). Therefore, Wix basically locks a lot of your SEO exclusively to them. Wix allows more flexibility than many other template builder websites, but it comes at a steep cost if you ever succeed enough to want to outgrow them.
As for the SEO aspects of using a builder like Wix, Google will definitely rank those sites, but I believe Google considers sites like that to be inherently mildly penalized as I've seen sites that don't change speed/quality/content move from Wix to a 'real' site platform like Wordpress and do better SEO wise.
It may be best to simply use Wordpress to get started with a simple template that likely doesn't allow a lot of customization but at least allows you have to legit URLs and can grow and scale your site more efficiently as that time comes.
I would like to add to this in addition to the other good answers:
I know your answer is mainly about SEO and important as SEO is, that's not the only thing to look at when choosing a framework.
Some things to consider right off the top for services like WIX, Weebly, Shopify.
Do you have full ownership of the site? No.
Access to a variety of tools (components,modules,plugins,expansion), active and knowledgeable community? Not, really (most widgets on WIX is made by WIX) and you are the first I saw asking about WIX.
Are there additional fees or monthly fees? Usually, yes.
Who is the target audience?
Wix is a drag-and-drop site builder catering to a beginner audience.
That pretty much tells you most users of WIX type templates are not people with SEO knowledge and so therefore SEO is not a focal point. Though there are some SEO tools, I think it is more or less to get credit for WIX since there is many instances of WIX in the source code. They make money up selling you with premium widgets and turn-key business solutions. In a sense, further enslaving your business/site having more features that would be disrupted if you were to leave, since there is no ultimate ownership.
Non Swappable Templates. This is mind blowing to me
In WIX, let's say you have your site all nice, just the way you want it, and for whatever emergency reason you have to swap the template. You have to recreate all the positions, sizing and colors, they are not preserved. WHAT!?
As for designing from scratch, my concern for you is this.
Since you asked what is better for SEO, with all due respect, it may be that Materialize or Bootstrap might be a difficult starting point. The build is more time consuming, and greater knowledge is needed as a starting point. From search and user friendly directory structuring or rapidly generating content, there is a lot more to deal with, and that is not including connecting it to a database.
You may want to consider The 3 Big CMS' (Wordpress, Joomla, Drupal).
All 3 have a lot to offer, from active communities, availability of tools, SEO is well thought of and effective, you have ultimate ownership, and most of the plugins you would need are readily available and free. Different learning curves based on who maintain the site, the web dev or the client(if applicable). WP being the most client-friendly (not so good for developers), Next, is Joomla, being more geared towards the developer, but still easy to use, followed by Drupal, more developer based and less user friendly based.