I recently went through this, I used to have a 1600 by like 900 or 1200 monitor with a 5ms delay, worked "fine" for me but it broke, so I went shopping and wanted something better, so I went with a 1ms ASUS monitor 1920x1080 (VX228 model) and it's a world of difference. The 1ms is noticeable in all games. The color scheme is hard to adjust, but so far it's been fine for Osu.
As long as you keep your Tablet mapping/Mouse DPI the same and keep it to the osu window there is so real "adjustment" period unless you downgrade from say a 1ms delay to a 15ms delay. Then there is quite the difference. From 5ms to 1ms wasn't though, just a noticeable improvement.
Just because the monitor is different size, doesn't mean there will be different hand placement. Your cursor will still move accordingly, just at a faster/slower rate depending on size difference you've switched to. Muscle memory will usually take over in a matter of minutes and your brain will adapt pretty fast. I also heard 144Hz monitors are awesome, but I can't comment, don't have one.
In short; there shouldn't be an adjustment period at all really (unless drastic difference in monitors). Just play some familiar songs when you first get it so the muscle memory is already there and you know what to expect.
Side note; If you're upgrading to a 27" make sure you're far enough away from it, because likely for anything 6 stars or above there will be screen wide jumps/jumpy maps and usually staring static in the center of the screen while jumping will cause misses, and you don't wanna have to move your neck/eyes like a madman. (assuming you go full screen or high resolution)