Greetings.
Both, Magento and BigCommerce are e-business platforms. The great difference is that in Magento you need to setup a server (owned or hosted) previously and Big Commerce you can use it as a service. While Magento software is free you have to pay a "rent" for the server or dedicate a machine to host the store, Big Commerce server comes in three editions, standard, plus or enterprise; each flavor is differentiated to the other due to the available tools and the transaction fee . But, each one is enough to build and run an e-commerce.
Having said it, in BigCommerce there are hundreds of themes to choose but with limited customization options (to fine tuning the store-owner preferences) or you can buy a theme from the Big Commerce marketplace. While in Magento the theme have to be brought, ensuring the compatibility with future versions of Magento.
In Big Commerce you have to pay as low as $79/month the Plus service (recommended) and with Magento a VPS with minimun specs server is as low as $60/month (paying the complete year in advance).
In Big Commerce you can forgot about configuration or backup, in VPS you have to administer your server. I tell you to show how my job will be do, because in both cases I can help and accompany you at every step, making the necessary adjustments to put your e-store online.
Is true that I'm a new freelancer, but far from being a weakness, it is my strength, because I do whatever it takes to get a positive rating.