Disclaimer: I represent Exp:resso (Store).
You're not able to use Matrix for product modifiers but in the vast majority of cases you wouldn't need to. Store's own modifiers matrix is fairly flexible providing a way to name your own modifiers along with optional individual or shared SKUs, optional price adjustments, and individual stock control. At present, the only main disadvantage is that you can't (as of yet) set dimensions and weights on a per modifier basis. The advantage however, is that you get ready-made {modifiers}{/modifiers} tags to use with all calculations handled automatically.
In terms of differences, generally you can get up and running much more quickly and easily with Store. In places it follows a convention over configuration approach to strike a nice balance between the time it takes to configure and the level of flexibility you have to build whatever ecommerce solution you need to build. Store (and CartThrob) work in harmony with EE to extend it rather than modify it meaning that you still have the power and flexibility of EE, custom channels, field groups, relationships, etc whilst adding ecommerce to the mix. All of EE's tags are still available to use as well as those of both shopping carts.
Products themselves are entered as regular channel entries in both Cartthrob and Store where you can use as many Channels as you need to group or divide your products as you choose. You're free to use EE's native categories or third party tagging addons to enhance grouping of products and relationships.
Store takes a different approach to Cartthrob when it comes to order management by keeping orders outside of EE's regular channels and into it's own database tables. This approach is adopted to provide an extra safeguard. Products are intended to be added and edited by users but orders should also be constant. Any accidental editing can quickly denormalise your order information. Instead they are viewed and Managed via Store's menu options. You still have the flexibility to add payments, change statuses, view and export, etc but this is one area where sensible defaults are applied to protect the data in the system.
For the vast majority of cases the combination of Store and EE provides all the flexibility you need to build your online shop exactly as you imagine. You can create product fairly complex product modifiers with their own stock levels and SKUs, use any number of custom fields to your products channel, set handling charges, product dimensions, multiple tax rates, etc. You can set your own shipping methods and rates or use any of the shipping extensions for live rates from the major postal services. You're also free to create your own extensions to extend this to use any other shipping company who provide an API to work with. The same applies to payment gateways where OmniPay is used under the hood (you can thank Adrian for that one too. In this case it's not a case of selling the by-products but giving them away for free :) ).
Store 2.0 saw the introduction of Sales and Discounts with many powerful combinations possible. Reports are included but for anything more detailed it's only an SQL query away.
Generally everything is built with extension in mind and for specialist requirements there are a growing number of extension hooks to take advantage of. If you need one which isn't included then drop us a line.
Documentation is good and releases are fast and frequent with new features being added all the time (there's plenty more in the pipeline!). We're always open to requests if you have any suggestions. Feel free to contact us directly, we're always open to feedback. As @JackTheKnife mentioned, we patrol this forum daily so you're free to post here or send us an email.
