Obviously it's going to depend on each specific project, and I can only talk from my own (store owning) perspective, but over the years I have evaluated and installed and played with just about every ecommerce system of significance on the planet today. The ones I've spent most time with are BigCommerce (in it's self hosted form before it went SAAS), EE & CartThrob, and Craft Commerce. I'm not going to slag off Magento as such or very specifically - although as I go through my points it should be clear I though about all of these with Magento, and found them lacking or painful...
Here are the reasons I chose Commerce, roughly in order of importance:
Pixel and Tonic - more than anything else, I think it was the considered, open and intelligent approach of Pixel and Tonic - that I carefully observed from 2012 to 2015 - that convinced me it was a solid, well thought our platform backed by some exceptional people.
Content driven ecommerce - basically, there are two types of systems in the world - either commerce systems that have a little CMS bolted on, or content systems with a little shop thingy bolted on.
For me it's essential that content, and absolutely great management of it, be the main thing. BUT, I also do want a great shop on top of that - with integration between the two that feels completely transparent and natural. This means, in essence, that a first party solution to both problems is ideal. When you have separation between the two, it always feels bolted on and shoe-horned in (see CartThrob or WooCommerce as prime examples).
The fact is pretty much anyone can set up an online shop right now and if all you want are product grids with pretty pictures, and lots of discount options, and simple (but simplistic) integrations to popular shipping services, then Shopify or similar is your obvious option. But if you want substantial, useful content (and anyone that wants to compete with Amazon etc really should!) - then you need a content driven approach. Expertise & Service are the keys to successful long term commerce in a world of box moving mega-discounters.
The ExpressionEngine (i.e. Content Modelling) foundations - before coming to Craft/Commerce, I was considering (and implementing) CartThrob with ExpressionEngine. And if I am truthful it's the fact that Craft grew from this approach - but then vastly improved on it - that gave me the motivation to spend serious time evaluating it (credit where it's due - Craft, like everything else, stands on the shoulders of giants).
I fundamentally think structured content modelling is the key to excellent content management, which is fundamental to 'more-than-average' shops....see above.
Matrix - the problem with structured content is that it can be TOO structured for long form content - you simply can't have a dedicated field for absolutely everything - and so where you DO want to write longer form content, it tends (on lesser systems) to be that everything just gets dumped in a WYSIWYG.
Matrix (and Supertable/Neo/etc :) ) - is the (so far) best solution to this problem. It gives you a structured-within-longform-content approach that is second to none. You can build very flexible page assembly systems using structure where you really need it and freedom where you don't. Which means you can build some wonderful content driven ecommerce stuff very quickly.
Cost & support. Magento - while open source and sort of free in a community supported sense/version, superficially looks good value. But if you add real support - the kind you need if livelihoods depend on things - it becomes fiercely expensive. P & T support is fast, unlimited, generous and easy to access.
Ease of implementation. Craft & Commerce, with Twig, is easy. It's really, really simple and logical to write your templates, and Craft always seems to behave in natural, expected ways. The more time you spend with it, the less gotchas you need to worry about. It's that rare system that gets better with familiarity. Magento has a reputation for being absolutely labyrinthe in scope and difficulty in terms of template implementation. I've heard the term 'horror show' used more than once.
Flexibility - Whilst Commerce doesn't support a lot packaging, shipping stuff etc out of the box, and where it does the implementation can feel a bit basic, the inherent simplicity of Craft plugins (and V3 looks to improve on this further a lot!) - means you can implement just about anything you need easily. In my experience for complex stores off the shelf things rarely meet real needs anyway - so what you really need is a well though out architecture for extension.
In terms of product & variation management, Commerce, like Craft itself, is wonderfully flexible and yet simple. You can create elegant, responsive content entry systems for your editors with ease, and separate your data concerns in sensible, long term maintainable ways. It nails content management as well as anything I've been able to find.
Personally, I think neither of them are good solutions for very simple stores - there are simply cheaper, polished, off the shelf things that do that well. No - these systems are for complex, bespoke e-commerce, where a substantial investment of time and money is used, to make something a bit special. For my money, Commerce is the flexible, powerful content driven approach that nails this problem. And Magento (in my limited experience of it) is an over complex, over priced, frustrating to work with alternative.
Apologies, this is a bit of a ramble. Someone should come along and write a 'The Commerce Advantage' to match the Craft one...but hopefully this helps a bit!