I suspect the answer to whether TypeScript is better than PureScript depends heavily on your relationship with Haskell. :) As to whether 1) TypeScript is a good language on it's own, or 2) better than the others we've tried for certain tasks, I can provide some opinions.
1) Is TypeScript a good language?
Short answer: Yeah, it's pretty good. Longer answer:
Microsoft knows their way around a compiler. The tooling is rock solid and well designed, so third party editors have no trouble providing a proper editing experience. Compile times are fairly impressive for the amount of verification TSC provides, and errors have always been fairly intelligible (if sometimes verbose). In all the time I used it I managed to trick the compiler into doing the wrong thing only once, and that was when it was still pretty new. The type system is intuitive, expressive, and pay as you go; which works well in a prototype-heavy environment like this. Finally, (and importantly for an open source project) anyone who can work with a JS stack can sight-read typescript pretty easily. Since switching from other more esoteric languages, we've seen a noticeable uptick of contribution from the community.
Of course, it's not perfect. You're still playing in JS land, with all the problems that entails. ES6 (which TS will happily transpile) lessens that blow, but you'll feel it nonetheless. Performance is still just JS performance, you're limited to JS data structures, equality semantics will still make you sad in situations that you can't statically guarantee, package management for the web is junk, etc. I also have some nitpicks about the generics system, but that's been improving of late and comes up so infrequently that it's hardly worth mentioning.
All in all, it depends on your use case, which brings us to:
2) Is it better than other languages we've tried for this?
More or less. The qualifier there is that different languages suit different tasks.
Eve has a pretty deep stack, from parser and compiler up to web components and other UX considerations. No one conventional language is really going to be best across that gamut. However, for initial prototyping the most important thing is reaching a proof of concept as quickly and obviously as possible. As mentioned above, TS excels at this. Once the new runtime has stabilized, we'll look into rewriting the executor (the most performance intensive portion of our codebase) in Rust and compiling to wASM. Rust is definitely a language worth your time if you have strict performance requirements, but it's a bit of a bear to get into, and it's compile times are not great (even with optimizing disabled). It's a much smoother process if you go into it with a clear picture of exactly what you're trying to build first. We also plan to pull the last mile UX into Eve itself along the way, but I expect we'll be keeping a middle layer of TypeScript for everything that doesn't quite fit on either extreme.
Lua's also a fine language, but without LuaJIT it's pretty slow, and with LuaJIT it's a bit unpredictable. I also stumbled into a couple LuaJIT bugs without trying very hard. That said, props to the LuaJIT team, as soon as I provided sufficient diagnostic info they got things patched up very quickly [1]. Just be prepared to get your hands dirty if you want to play in that sandbox.
We've talked a little about why we're not using Clojure/ClojureScript right now, but the gist of it is that while they're both great languages, most of the features that make them nice are too slow for us to use even outside our hot paths.