I'm both a Wix Legend (top level web design partner) and a Shopify Design Partner and have designed many sites on both platforms. Both have good bits and both have bad bits and so here is my honest and unfiltered opinion on which platform you should use to host your online shop.
Pro's (+) & Cons (-)
+ Easy to use
+ Cost Effective
+ Very bespoke home page and rest of site
+ Can sell digital products/downloads
+ Basic stock control
+ Great starter shop
- Basic options - for example, colour and size
- Templated and rigid store pages that can't be edited easily
- Not good at creating bundles of products - for example, selling a picnic hamper with different options as the stock control isn't sophisticated enough to handle it
+/- Reasonable SEO
- Basic category set up
- Definitely not geared up for a lot of products or categories
- No good for anyone selling personalised goods or products that can be configured
- Search is pants! No other way of putting it, finding a product isn't easy and that makes life difficult if there are a large number of products. In a small store that doesn't matter.
In summary, Wix does what it needs to do on a fairly basic level, I love the fact that you can still have a fabulously designed site with a nice looking basic store at entry level pricing. However it's nowhere near sophisticated enough to deal with a large number of categories or products. We can't have sub-categories currently and so if you have a large number of products categories can get unruly very quickly either by having a large number of products in each category or worse having a large number of categories and finding it difficult to find anything. Search is virtually non-existent (even the add-ons). I'd definitely recommend to anyone who has a small number of products and is just setting out. Wix is a great starter store.
Pro's (+) & Cons (-)
+ Very flexible has an app or add on for virtually anything
+ Nice clean templates that can be customised for most stores
+ Big template library if you want something a bit "more" than the standard free templates, all designed especially for Shopify and easily installed, prices are moderate
+ Great for anyone that needs highly customised products or personalised gifts or clothing, although you will need to pay for a plug-in or add-on to do it
+ Good stock control
+ Can have categories and sub-categories making it far easier to organise your store
+ Excellent product search
+ Massive amount of drop-shipping options meaning you don't even have to carry stock you can just sell other people's by "plugging and playing"
- Everything is an add on (and I mean everything) often with additional cost
- Templates can be edited but their flexibility is very restricted when compared to Wix
- Shopify at their base level is much more expensive than Wix
- Adding additional pages to the site (for example About Us or Look Books) is very basic
- Virtually no flexibility to create your own contact forms without paying for an app or add-on
- Cost of running the store can quickly add up
In summary, I'd say that Shopify is a more "grown up" ecommerce platform, it is better for those with larger portfolio of products or who require say personalised options and better stock control along with integration with POS etc. However it is much more expensive to run, for example, if you wanted to have a look book or gallery on your site - then you'd have to pay for an add-on (there are a few free or cheap versions but they carry the app creators logo and are usually very very basic. Even editing a contact form is impossible at the time of writing, although again you can pay for more advanced features. On the plus side it is far more sophisticated, you can have sub-categories and search is a million times better.