The 7X57 Mauser was the first modern round, beating the 30-30 by several years. You can make a good argument that nothing better has come along since. It has taken every animal on the planet, probably as many elephant as most any other round. And it has the range for long range shooting of smaller animals.
The 7-08 duplicates its perfromance and light recoil, but in a smaller package, with better accuracy. I don't own a 7-08 simply because I started with 30-06 and 308, but I consider it to be about the perfect all around chambering. I have too much time,money etc., in my other rifles to change at this point in my life.
As others have correctly noted, any short action rifle can be built coniderably lighter than a long action rifle. Many manufacturers do not choose to do so and build identical weight rifles in both. If choosing between a 7.5-8 lb rifle in either 7-08 or 280, or between 308 and 30-06 it makes no sense to buy the short action. But given the option of a 5 lb short action vs a 7.5 lb long action, I'll give up 100-150 fps to get the smaller, lighter rifle.