What benefits would I need to see in an eCommerce platform to migrate my shop to it?

If you’ve got to the point of deciding on which platform should you migrate your shop, probably you’re dealing with (at least) one of the following situations:

the platform you’re using is rigid, expensive, and difficult to maintain;
the lack of platform features blocks you from innovating and keeping up with consumer demand;
you need an out-of-the-box website to stand out on the market.

Top benefits you should analyze before picking a new platform:
flexibility to add additional channels;
intuitive activities and content control through the dashboard;
features that allow personalization and customization;
fast and secure integrations with 3rd party tools and services;
features to localize and analyze the content’s performance.

Why use Magento
easily manage the product catalog;
secure platform, with periodical updates;
free license (Open source);
responsive interface;
strong architecture - if tweaked, the platform can handle huge product catalogs and traffic;
elastic search integration out of the box;
integrates with a lot of 3rd party systems (ERPs, CRMs, other management software)
integrates SEO, marketing, and promotion tools;
access to the largest community and to a variety of modules.

Why use Woocommerce
efficiently manage the content of your online store (being a platform derived from WordPress);
open-source eCommerce platform;
easily integrate and manage the web site’s products and catalogs;
access to various design templates;
standard plugins available (free or premium) for payments, deliveries, social media, email marketing platforms, Analytics, etc.;
fast time to market;
optimal price-quality ratio.

Note that migrating e-commerce platforms is more than moving data!
I strongly recommend you hire a professional tech team to avoid high-risks like data loss and long downtime.
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Stefan Nicolae
Head of Ecommerce @Roweb