The high refresh rate monitors would work best if they are G-Sync or FreeSync enabled (eliminating screen tearing for a smoother gameplay by adjust the monitor's display rate to what the GPU graphics rate can provide). I am assuming with those 2 monitor options, you have at least a GTX 1070 GPU?
For the 1440p ultrawide (assuming 34"), the pixel density is greater per inch of screen and view will be more "zoomed out" but drawback is texts/icons will appear smaller. For the 1080p ultrawide (assuming 34" too), the pixel density is lesser, often resulting in "pixelation", view would be slightly "zoomed in" but texts/icons will be larger. Hence, one major factor to consider between these two monitors (assuming both are 34"), is the distance of the monitor from your vantage point (as well as your desk space).
The 1440p would have to be placed a bit closer to your eyes (about less than 24") for visual acuity; the 1080p (again assuming 34") can be placed a bit farther from you (more than 24") and would have the same visual acuity as the former.
Another factor to consider is the graphics power needed to render a 3440 x 1440 (i.e., 4.95M pixels) versus the 2560 x 1080 (i.e., 2.76M pixels). The GPU will "work twice as hard" on the 1440p than in the 1080p. So, you would expect lower framerates gaming on the 1440p compared with gaming on the 1080p using the same GPU.
If you watch movies from a distance from your monitor, I highly suggest the 34" ultrawide (rather than the 29" ultrawide, if that's the size you are considering for the 2560 x 1080). The 29" ultrawide, as I mentioned previously, is just a 23" screen with extended sides. Movie looks small when viewed afar than in my 27" screen.