If you aren't already in an ecosystem (mainframes or AIX), the obvious question is: what does a different architecture offer you, how well is it supported by what you use and and what does it cost you to migrate. In reverse, typical benefits of x86 are a) wide support in nearly all software, b) multiple suppliers of chips, c) large number of suppliers of systems at all kinds of sizes and specializations.

POWER systems have high memory bandwidth and can take really large amounts of RAM. You're limited to what IBM sells then, but the x86 market at that top end also isn't that large and less standard: Many companies will sell you 1-2 socket servers with 64-512 GB RAM, but if you want >3 TB its getting thinner there too, so also less benefit from using x86. So POWER is an option there, if running Linux the difference for sysadmins isn't that large. And e.g. SAP supports it for their HANA in-memory database, so enterprises might buy them there. At the same time, lots of enterprise software doesn't run on them, so they're unlikely to fully migrate.

Then there's companies building their entire stack themselves and operate at a large enough scale that some porting costs are acceptable if it brings them a benefit. They'll always be looking at alternatives. Google is known to have experimented with POWER systems. Cloudflare afaik is using some ARM systems because they turned out to be the more efficient choice for them. At Google/Facebook/... scale, it's likely also a signaling tool when buying: Intel is more likely to give them what they want if there's a somewhat credible threat of them replacing part of their systems with non-Intel.

I don't think there's much competition between x86 and s390. You'll use the later only if you're already an IBM mainframe customer and don't plan to migrate off.

For Power vs x86 it probably matters a lot what type and scale of operations you're at. As far as I can tell x86 typically has the better price/performance ratio but then I think there are quite a few supercomputers that use Power so there must be some advantages (probably mostly I/O related).

I have worked for companies that used both. Based on those experiences:

Use Power RISC with AIX in established IBM user organisation that wanted to run Unix software so we ported existing software to AIX.

Use existing s390 system running several core systems, to run Unix partitions to deploy software already written for Unix in C.

I have never even heard of any company not already being an IBM account migrating to either of those systems. The capital and operating costs are typically far higher than for comparable performance x86 based deployments. Technical staffing is much harder still.