Necro-ing this as I had the same issue, and it came up on google. I believe sensitivity should be the same. The problem is the letter-boxing and resolution is implemented differently in lazer.
1. To keep your sens from stable to lazer, set your resolution to the native resolution of your monitor.
2. Adjust horizontal and vertical position to the middle values to center your play area.
3. Adjust horizontal and vertical scale to get the letter-boxing effect in stable.
4. Bonus setting, set your Frame Limiter to "Basically Unlimited" instead of "4x refresh rate." I think I noticed a difference in input lag.
The actual reason the sens feels different is because if you set a lower resolution in lazer, your dpi will be affected greatly because resolution is handled differently (notice the pixellation in lazer, whereas a letter-boxed, low resolution will still look crisp on stable). In stable, you can set the resolution to 1280x1024 instead of your native resolution which will do the letter boxing, but it still
renders the game using your native resolution from one of the settings. Setting the resolution 1280x1024 on lazer is not necessarily the same as a 1280x1024 osu! stable rendering at native resolution. After fixing these issues, lazer has become much more playable and easier to migrate to with a mouse. Without messing around with these settings, it was just unplayable.
Lazer Settings
https://imgur.com/N2bclWlStable Settings
https://imgur.com/0mLYPwrTo get your letterbox conversion. My native resolution is 2560x1440. To preserve stable's 1280x1024:
1280/2560 = 50% horizontal scaling
1024/1440 = 71% vertical scaling