I've done a safari with only the 375 that included plains game (don't they all?) I've done a safari with the 375 when the Mrs brought her 308. It is nice to be able to grab the 308 for the smaller stuff like wartys or impala and Mrs Blacktailer has used it on animals up to zebra which are tough critters.
OTOH I have used the 375 on deer, pigs and varmints in NA and it is not unpleasant and gets the job done.
The 375 will take care of anything on either continent, the 7x57 will take care of anything on either continent also but is not legal in most areas for DG and is certainly on the light side for big bears.
Pick whichever you are most comfortable with.
