In my extensive testing in the past, I have dubbed this phenomenon as "text jiggle". Unfortunately, it is not something that can be easily controlled. One way to minimize it is by assigning an explicit line-height, particularly in pixels, to each text element.
The default line-height can vary significantly across different browsers and for different font families and sizes. By setting a specific line-height, you can address this issue.
However, even with a defined line-height, the exact positioning of the text within the line-height space may still vary slightly from browser to browser. While some font-size and line-height combinations may display consistently across all browsers, others may differ by a few pixels. For example, Arial at font-size:11px and line-height:14px may look the same in Firefox, Webkit, and IE, but changing the line-height to 13px or 15px could result in a 1px difference.
There is no standard behavior for this inconsistency. It ultimately depends on how the specific font-family, font-size, and line-height are rendered by the browser on a particular operating system. For instance, Arial tends to be relatively consistent with minimal variation as long as an explicit line-height is specified, whereas Helvetica can vary by as much as 4 to 6 pixels.