In the web-app/API dominated world of modern software development what advantages and tradeoffs would a CL have over Clojure?

CL over Clojure: it's the OG Lisp that the creator of Clojure used and wanted to continue using but faced too much resistance from management afraid of anything not-Java/not-Oracle, or not-CLR/not-Microsoft, etc. Clojure shipped originally as "just another jar" so devs could "sneak" it in. If you don't have such a management restriction, why Clojure? If you want to integrate CL with the JVM, you can use the ABCL implementation, there's also something from one of the proprietary Lisps. Some useful CL features that are nice in this domain: conditions and restarts mentioned in a sibling comment (very nice to help interactively develop/debug e.g. a selenium webdriver test), ability to easily compile an exe (perhaps useful for microservices, or just to keep your deployment environment clean and not having to care about Lisp), and ability to easily ship with an open local socket allowing you to SSH in (or SSH port forward) and debug/fix/poke around in production (JVM of course lets you attach debuggers to a running process, even certain billion+ dollar companies will have supervised/limited prod debugging sessions for various hairy cases, but it's not as interactive). You should never hear CL advocates claim you can't scale to large teams/groups of engineers or large multi-million-lines sized projects, though you might oddly hear Clojure advocates sometimes claim you can't (and shouldn't) scale to such large projects -- large groups of engineers are a non-issue for them as well though, the challenge is in hiring, not in the language somehow making it impossible to modularize and keep people from stepping on each other.

Clojure over CL: its integration with the JVM is nicer than ABCL's, so if you do actually want a lot of the great world of Java stuff, it's easier to get at/you don't have to make a choice to enjoy things like state of the art GC or concurrency support. Database integration libraries are better. Clojure's philosophy of values are values is so much better. Access to libs (Clojure or Java) is via Maven, so it's a larger ecosystem with more self-integrating components (especially around monitoring/metrics) than what's available for Lisp via Quicklisp. Clojure is very opinionated, much of it quite tasteful, and that gives the whole ecosystem a certain consistency. (You can have immutable data structures in CL, you can if you want use [] for literal vectors and make them syntactically important e.g. in let bindings, but not everyone will be on board.) Even though its popularity seems to have stopped growing, at least at the same rate as e.g. Go which it was keeping pace with for a while, it's still popular enough with a bigger community; as a proxy measure there are multiple conferences around the world and good talks at adjacent conferences, whereas Lisp mostly just has one conference in Europe per year and only occasional the occasional project branching outside of that.

If you're doing a client-side-heavy webapp, ClojureScript is still amazing, CL's answers there aren't very compelling with the exception of CLOG (https://github.com/rabbibotton/clog) which takes an entirely different direction than the usual idea of translating/running Lisp on top of JavaScript and its popular frameworks.