Hi Peter, good question.
A template website will often look fairly professional to people viewing the site, the main difference is within the code, and it is the code that search engines and screen readers look at rather than what the site looks like.
A template built using a WISIWIG (what you see is what you get) editor will insert lots and lots of unnecessary extra code, this means that the file size is bigger, it's slower to load (not such a bad thing on broadband but if people are accessing your site through a mobile phone it is), it uses more bandwidth, search engines won't rank it as highly, web users with sight difficulties who use screen readers won't be able to read it, there is a good chance it will not look correct on all browsers and it won't meet W3C web standards.
The main difference to a website owner will be when they want changes made to the site. If the site is coded and uses a style sheet, every single page will use that same style sheet. To make a change you simply make it within the style sheet and it automatically changes every page within the site. Templates will not usually have as style sheet and changes will have to be made to every single page. A developer who has built the site from scratch will be able to make any changes, add new pages or make it so that you can edit the content yourself a lot more easily and quicker than amending a template.
Developers who use WISIWIG editors are not really developers at all, anyone could use one within about half an hour of opening it up and build a site within the hour (it's just a case of copying and pasting your copy across into it and adding images). Learning all the different programming languages as well as search engine optimisation techniques and keeping up will all the latest technologies within an ever changing industry takes years.
The other thing is cost; I've seen a lot of companies sell 5 page template websites for a low fee such at £29 but then charge £40 per month. Over a year this comes to £509 and they will then continue to charge you £40 per month as long as you have the website. A 5 page site from us will cost you £299 but that includes a years hosting, after that year hosting will only be £5 per month so it actually works out a lot cheaper in the long run. I will also spend time looking at your site and checking it's visitor stats and assessing where it could do better to help you get the most from your website. We are also currently allowing people who buy a 5 page website from us now to pay for it over 6 months.
If you can find a very cheap template site and the website is a personal or a family one then I'd say go with that. However if it is for business I would always go for hand coded. If your website can easily be found on Google then your sales will almost certainly rise by a lot, compare this to the cost of advertising in other, more traditional ways.
I hope this answers your question, if you have any more I'm happy to answer them.
Kind regards
Adam
P.S. You can view a websites code by right clicking on the page (providing its not Flash) and then clicking View Source. You should hopefully be able to see the difference between my site and this one for example pigscorner . com (I can't post links yet as I've not written 15 posts).