In addition to the data from Denmark, an analysis of the data from England found no significant association between Omikron and hospitalization: https://www.imperial.ac.uk/mrc-global-infectious-disease-analysis/covid-19/report-49-Omicron/
Note that this doesn't say anything about need for intensive care or ventilation, which seemed to be lower among hospitalized patients in the South African data.
Still, given this data, and the caveats of the South African data (younger patients, very high levels of natural immunity), I would set the chance that Omikron is ...
I don't think the Danish numbers are comforting at all, and I believe that the tweeter is comparing apple to oranges. The latter numbers cited, which are now at 91/18941 (0.48%) versus 1794/127060 (1.41%), are the total number of admissions in patients testing positive between 22. November and 15. December. Since the 14. And 15. of December have most of the positive Omicron cases, but the Delta cases are more spread out, we should expect the number of hospitalized Omicron cases relative to Delta in this cohort to rise as the disease runs its course.
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