The AW3418DW is an ultra-widescreen monitor. It uses a 21:9 panel with a higher pixel count (3440x1440) than a traditional monitor of similar size. Running this monitor at higher frame rates may be difficult as a result. The AW2518H is a conventional Full HD (1920x1080) display capable of running at 240 Hz, and a GeForce GTX 1080 Ti should not have much trouble pushing towards the high end of the refresh rate range at this lower resolution.
For competitive (eSports) gaming, higher refresh rates at moderate resolutions are generally preferable over high resolutions at lower refresh rates. Curved ultra-wide monitors are great for immersive gaming experiences, but for eSports, it's more important that you can react quickly to your opponents. The higher refresh rate helps you respond faster and gives you smoother motion, making it easier to keep track of the action. (More technically, a higher refresh rate means there's less time between each frame displayed, so the action appears on the screen faster.)
Furthermore, the AW3418DW uses an IPS panel with slower response times than the TN-based AW2518H. Although TN displays suffer from narrower viewing angles and lower color accuracy especially when viewed off-axis, they have faster response times, which results in less ghosting and motion blur. That, too, will make it easier to follow fast action during intensive gaming. IPS panels are great for color-critical professional applications like photography, and while though there are gaming-oriented IPS displays (including the AW3418DW), they can't achieve the sorts of response times the best TN panels can deliver. (Trust me, I know this first-hand after upgrading from a cheap IPS display to a Dell S2417DG. The faster response time is something you notice right away, even if viewing angles do suffer a bit.)
If yoy're looking at the Alienware 25 monitor, make sure you're buying the G-SYNC version (AW2518H) and not the FreeSync version (AW2518HF). The former is more expensive but since you have a GeForce card and not a Radeon, you'll need the G-SYNC display for the best experience.
Ultimately, while your choice of monitor is a major factor in overall latency, it is not the only thing that matters. This answer has more information about how different sources of latency can add up. In short, latencies from your processor, graphics card, the monitor's internal processing ("monitor input lag"), display response time and refresh rate, and even your mouse, can all add up.