It's harder to express complex grammars in combinator form.

Combinators excel best for relatively simply regular languages (eg., json, html, etc.).

Languages with lots of "modality" in parsing, ie., context switching, are easier to express in generator-form (eg., antlr).

One of the main differences is that LALR parsers don't use backtracking to implement "choice". Parsing happens in a single pass over the input. With parser combinators, ambiguity is silently resolved by accepting the first option that the parser tries. Bottom up LR parsers also do a better job of dealing with left recursion, compared to top down parsers. If you want to parse something using a recursive descent parser (or combinators) you may need to rephrase the grammar to avoid left recursion.

Some of the main downsides of LR parsers are that you need to use a parser generator and you have to know how to resolve possible shift/reduce conflicts. It's more complicated than top down parser, which is just a bunch of regular recursive functions.