As an early medievalist, I tend to use BCE/CE in my own writing. It lets me communicate a date that everyone understands while giving tacit acknowledgement that (1) there's no universal consensus about the actual birth year for the historical Jesus, which is nominally the basis for this calendar, (2) many of the people I study weren't Christians, so it would seem odd to impose a Christian calendar on their lives, and (3) even the Christians whom I study didn't universally use the BC/AD calendar, which was still being used alongside other methods of dating such as regnal years or years since Creation.

That said, some journals and publishers in my field continue to prefer BC/AD dating, while others prefer BCE/CE or even AD/AH (for giving parallel Christian and Muslim dates). So there's no hard rule, it depends on who your audience is, and few people I know have firm preferences.

Confirming what textandtrowel said. It boils down to personal preference and adherence to convention. I've only ever used BCE/CE in the past decade, and probably run into it in the majority of cases in English-language literature where it needs to be specified.

If you're writing in English for an Anglophone audience, everyone will likely understand BCE/CE just fine. It's been common for a long time now.

However...

Has most of the world now switched to BCE/CE or are many still using BC/AD?

...I'm not sure where "the world" would really fit though, since numerous other dating systems exist and are in common usage throughout the world.

In Dutch and German, I've never seen BCE/CE used.

As a historical North American archaeologist, I tend to use CE. Precontact North American archaeologists use BP (before present..which is set at origin of radiocarbon dating, 1950). You also see a lot of RCYBP, “radio carbon years before present”. Is BP used in old world archaeology?

Since they both mean the same thing it mostly comes down to personal preference. BCE/CE is mostly an attempt to make the calendar less explicitly Christian.

I tend to still use BC/AD but that’s largely just because it’s what I’ve always used. I’ve never had a teacher, professor, or advisor that took issue with it.

I try to always use BCE/CE - I find that students have a poor understanding of BC/AD. Very few can define what it means. Plus, it weirdly leads to confusion - that I could see compounded in some of the comments here. Students get to thinking that AD means "after death" (or using other abbreviations: after Christ/Jesus) - which leads them to thinking there is this 30+ year period of time that is "Jesus time" that comes after BC and before AD.

using BCE/CE - appears to avoid that (I guess because it makes them rethink it)