The US compared to the UK has had ~13.6 more shootings and ~29.4 more injured/dead in the last 23 years.
The population in the US is ~5 times bigger than in the UK. I would not call that it’s literally on PAR per capita, I would call that a whole lot more.

UK population: 66,971,411
Mass shootings:

Year	Shootings	Injured and dead (total)
2020s	8	41 injured or dead (total)
2010s	9	67 injured or dead (total)
2000s	1	5 injured or dead (total)
18 shootings and 113 injured or dead in 23 years

US population: 333,287,557 (~5 times more than in the UK)
Mass shootings:

Year	Shootings	Injured and dead (total)
2023	24	270+ injured or dead (total) This includes the most recent shooting, thus the plus sign. (This is more shootings and injured in one* year in the US, than the last 20 years in the UK).*
2022	24	340 injured or dead (total)
2021	14	144 injured or dead (total)
2020	8	59 injured or dead (total)
2019	18	223 injured or dead (total)
2018	18	232 injured or dead (total)
2017	17	663 injured or dead (total) (61 dead, 411 injured in the Las Vegas shooting, that leaves 191 total)
2016	12	197 injured or dead (total)
2015	13	159 injured or dead (total)
2014	5	60 injured or dead (total)
2013	6	52 injured or dead (total)
2012	14	202 injured or dead (total)
2011	6	66 injured or dead (total)
2010	6	45 injured or dead (total)
2000s	59	608 injured or dead (total)
244 shootings and 3320 injured or dead in 23 years

I cannot find similar data from Europe as a whole.

Sources:
United_States (Wikipedia)
List of mass shootings in the United States (Wikipedia)
United Kingdom (Wikipedia)
List of mass shootings in the United Kingdom (Wikipedia)