Now that Zed is open source they're actually quite similar in capability (even sharing a number of underling libraries). The biggest difference is probably that

Now that Zed is open source they're actually quite similar in capability (even sharing a number of underling libraries). The biggest difference is probably that Zed is backed by a commercial company (and I believe they have plans to sell collaborative functionality on top of the core editor) whereas Lapce is more of a community open source project. Lapce is also cross-platform whereas Zed is currently macOS only. But they seem to be making rapid progress on linux support so this may not be relevant soon.