Not really. The usual measurement is kg/kW, so You have to divide the weight with the power. According to solo-germany.com, the weight of the 681 is 6.6kg and power is 4.7kW, so it is 1.404kg/kW. I think "on the paper" the best one is the new Stihl MS661 (from stihl.de) 7.4kg/5.4kW=1.370kg/kw. Stihl MS660 is 1.404kg/kW (from honeybros.com, as stihl.de doesn't include it no more); MS461 is 1.523kg/kW.
But from personal experience there is definately more to this than power and weight. I always consider vibration levels of the saw as well, because those can wear You out faster than the weight of the saw. That's why I sold my MS660 to get 390XPW, and there hasn't been a day I have regretted it. Really like the 390XPW.
Have to admit - those SOLO 681 stats are very good.