This question is more complex that it looks like, there multiple aspects of it.
Compatibility (for 3rd party developers). First of all ETC is keeping tech compatibility with ETH, on API and EVM level. But only things that don’t compromize security and decentralization of ETC. For Smart Contract and DApp developers it means that nearly all of apps can be launched on Ethereum ETC. Most of development tools and libraries are compatible with Ethereum ETC. Basically if you see that a tool for developers is for Ethereum, it means it will work on both Ethereum ETH and Ethereum ETC, as well as on private Ethereum-based networks and most of Ethereum forks. So technically we have multiple public networks, compatible with each other in 99% cases. Notice that it’s compatibility for 3rd party developers, which means that there could be difference in mining aspects (if ETH will move to ProgPoW or PoS)
Different priorities. The main difference is Ethereum ETC philosophy, which is close to Bitcoin, and ETC community cares more about security and decentralization. It affects all decisions and future path of Ethereum ETC. For example ETC community is agains any ad-hoc changes to non-techical aspects, and things like “foundation decrease monetary supply threatening by difficulty bomb”, is impossible in ETC. It’s basically a crime in a real word (battery or robbery, you force another party to sign unfavourable contract by pointing a gun to their head), that’s another reason why such things are not acceptable in ETC. More to that, ETC community decided (literally community, not developers, it took a year of debating) to implement a predictable and objective monetary policy (ECIP-1017) and removed difficulty bomb at all, in two separate forks to avoid any interference between them. That’s just an example of priorities and how them affect development, so even if tech is mostly compatible at this moment you can expect different paths. Foe example ETC doesn’t plan to move to any PoS at this moment, because PoS is much less secure and brings centralization around big capital (and early investors, which got 70% of ETH supply).
Decentralization and Immutability. It’s mentioned few times here, so want to elaborate on it. ETC believes in the principles of immutability and decentralization because they are the main value provided by a blockchain. Any blockchain without the guarantee of immutability would be competing with Amazon AWS, which is already much more user friendly and a thousand times cheaper. Building a centralized/managed blockchain is a waste of resources, because it doesn’t solve any current problem without being 1,000,000 more expensive on every aspect of operating. (number is not random, it’s estimation and comparison with existing tech, made by Vitalik Buterin)
Multiple teams. Another aspect most people don’t realize, is that in ETC there is no foundation, no central organization, no leader, and all development is done by community and multiple development teams, each has own independent financing. Sometimes they work on different blockchains, including ETH. So should speak about particular team and project.
New projects. Now speaking about actual projects which are developed inside Ethereum ETC (thought they’re compatible with Ethereum ETH in most cases), I can give some examples from ETCDEV, which is a leading company there. ETCDEV developed few new technologies from scratch, such as Emerald Platform, a javascript react-based framework to build distributed applications and SputnikVM as a standalone, modular, embeddable and IoT ready EVM. Also ETCDEV is working on Orbita projects, which is going to to be a sidechain based technology that should fix scalability limitation without compromising security of the mainnet. It should be mentioned also, that ETCDEV believes in different market for Ethereum ETC, notable distributed computations and decentralized networks, such as mesh networks and IoT.
As a summary. Ethereum Classic is technology compatible with Ethereum ETH, but following different goals, such as decentralization and immutability. ETCDEV is working hard towards protecting Ethereum Classic from the potential interference of any centralized authority, by working on open standards and avoiding any features or functionality that may be leveraged to achieve control of the blockchain by any single party or coordinated group