From what I've read, 27" is a bit large for 1080p and you could potentially see image degradation (getting to the point where the image is being stretched out), but I image it's easier to see that when you have a 27" sitting next to a 24". I'm going to assume your old monitors aren't IPS since they would have been pretty expensive back five years ago, but the model(s) you've linked to are IPS -- Which is what makes them a bit more expensive. Regardless of whether you choose to stick with 24" or move up to 27", you're going to see a nice upgrade in image quality and viewing angles if/when you make the move to an IPS panel.

TL;DR - The max monitor size I'd go with for a 1080p resolution is 24", and if I was moving to a 27" panel I'd also bump the resolution up to 1440p, but increasing the resolution is going to require that your hardware work harder -- Assuming you increase the resolution of your game clients while multiboxing.