Answering my own question: Wikipedia has interesting graphics comparing the extend of the empire under the two emperors. Although the maps are not of the same size (Trajan's is slightly larger) there is very little to choose from between them. Current Iraq is missing but there are additional conquests in Scotland, Africa and Arabia.
From Historum.com (authorSylla1)
"Contrary to common belief, the maximal extension of this empire was reached not during the little more than two years (114-116) of nominal military occupation of the Parthian Mesopotamia & Armenia, which were never "romanized".
The maximal effective extension of the Roman Empire was under Severus I, when large portions of land of Mesopotamia, North Africa and the trans-Danubian border were acquired in a more stable (centuries-long) way, i.e. they were regularly romanized.
For some months under this ruler (208-211) most of Caledonia was militarily occupied too; naturally, it was never romanized either."