When troubleshooting anything information is key. The more information you can get, the better. Right now there is quite a lack of information on this other than the operating system and browsers used.
Operating systems should never have any effect on how a webpage is rendered. Different browsers can cause this to vary but that's not all that common (thanks to web standards!).
The alt tag and its text are designed to be displayed when an imagine cannot be displayed/loaded on a page for a particular user. This could be due to an unsupported image type or setting/config that could be preventing certain images from being displayed. So the first thing I would investigate is the file types for any images not being displayed. If there is no pattern then you might want to move on to seeing if the images are even able to be displayed at all in your linux installations of Firefox and Chromium by right-clicking and trying to either "Show Image" (Or "Display Image", all depending on the browser) or even open the image in a new tab. If the image simply can't be loaded at all (in any browser on your installation of Ubuntu) it may be related to something more involved (such as a setting/config or even something relating to the request sent by your computer).
I'm also curious as to whether the situation is universal for all browsers in your installation of Ubuntu or not. Try using or installing another browser or two just to see if it's actually system wide or if it can be narrowed down to specific browsers.
It's always hard to troubleshoot a problem in advance so I'm afraid there isn't much more I can tell you. It's an interactive process and each next step depends on what happened in the previous step.