Hi @Bhuwan_B, I've checked this on vanilla AEM 6.5.10 and on both browsers Chrome (version 98.0.4758.80) and Firefox (version 96.0.3) it looks it works the same on both my browsers - styling of pasted text remain. So I do not see the issue you have described.
Nevertheless according to Adobe documentation [1] using browser mode as a default one is not recommended.
Maybe you have some specific configuration in your Chrome or plugin that affects the result of paste operation.
If I good understand how browser mode works - I would say it is a bit risky in terms of result - because each user can have different browser version, configuration or set of plugins - so you are not able to predict how it will behave.
[1] - https://experienceleague.adobe.com/docs/experience-manager-65/administering/operations/configure-ric...