I've never used 21:9 before but from what I gather you get to see more so its got to be better right?
As was pointed out, not all games will necessarily support that aspect ratio, especially older titles, in which case you would end up with black bars to either side, and a smaller viewable area. The same goes for online video, which will typically have a 16:9 aspect ratio.
As for "seeing more", it's possible to run an ultrawide resolution like 2560x1080 on a 2560x1440 screen, with black bars to the top and bottom, though you may need to add a custom resolution to enable that. Some games also allow the field-of-view to be increased in their settings without actually changing the aspect ratio.
In terms of the physical screen size, assuming those diagonal measurements are not rounded, the 31.5" 16:9 screen would provide the most total viewable area of the three, being slightly larger than a 34" 21:9 screen, due to the way diagonal measurements work at wider aspect ratios. Again, it's not precise, since those diagonal measurements are likely rounded a bit, but the dimensions of those screens would work out to around...
(31.5" 16:9) 27.45" × 15.44" = 423.99in²
(34" 21:9) 31.36" × 13.13" = 411.76in²
(27" 16:9) 23.53" × 13.24" = 311.5in²
You'll notice that the 34" 21:9 screen is the widest of the three, but might actually end up slightly shorter than your existing screen, or at the very least, will be roughly the same height. Whereas the 31.5" screen increases the dimensions in both directions compared to your existing panel, since they both share the same 16:9 aspect ratio. And of course, this means that for 16:9 content that gets black bars to either side on the ultra-wide display, the image will appear no larger than on your existing screen. There's a nice little calculator at this site that lets you enter a screen's resolution and diagonal measurement to easily compute its dimensions and things like pixel density that you might find useful...
On that note, the 3440x1440 screen would have the highest pixel density, since it's packing around 34% more pixels into an area slightly smaller than the 2560x1440 screen. So, the pixels will be smaller, making the image a little sharper compared to the 2560x1440 display, at least when running content at native resolution. But you might also be more likely to need to make use of upscaling from a lower resolution, since rendering 34% more pixels will be more demanding on a given graphics card.
It's also worth noting that the different panel types each have their advantages. VA panels can display darker blacks than TN or IPS, typically resulting in a notably better true contrast ratio when viewed in a dim environment. However, those darker blacks usually tend to have slower response times, which can potentially result in ghosting in dark areas of a scene. That can vary between models though, and there are some VA screens that don't exhibit that issue. And IPS panels can often offer more accurate colors and better viewing angles, but again, there are exceptions. It's probably worth checking detailed professional reviews of the exact models of screens you are interested in, if they happen to be available.
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