If you have a wide monitor and several tabs open, having both scroll arrows to the right leads to a lot of mouse movement. Moving the “left” arrow to the left side will result in less movement, and is, imho, more intuitive (look at Firefox for an example).
Also, when you have more tabs than what is visible, the one you switch to is automatically scrolled to the right, even if you previously had scrolled it to the left. This is annoying and click-festy. Example: You have tabs 1-30 open, with 1-15 visible. You want to work on 16-30 and scroll the tab row to show these. BUT, when you click on tab 16, the tab row scrolls back to showing 2-16.