I don't think Higgs is really widely considered monumental in the same was as those other people. He had one good idea (at essentially the same time as Brout, Englert, Kibble, ...) which got his name attached. But I am a professional physicist and know none of his other work, in contrast to Dyson, Weinberg, Witten, t' Hooft, ...

Higgs is absolutely a more familiar name than the others, and stain too, whether you think his contributions were proportional to that recognition or not

That he has greater name recognition amongst lay people doesn't make him a monumental physicist.