Tbh I just taught dd2 the old method. She had 4 sheets of 20 each of those to do. She did the first sheet the grid method. Took her an hour, with about 75% accuracy, mostly silly errors in adding up or forgetting to multilpy by 30 rather than 3.
So I showed the the old method. Despite being tired by this point, she then did the other three sheets in 10 minutes total with 100% accuracy.
I calculate that to be just under 20 seconds for each one? I have just timed myself doing 314 x 34 by that method and including all the writing out and the adding up of numbers in the grid it took me 40 seconds. I am a qualified accountant so reasonably numerate
I didn't know what gridding was so I had to look it up here: www.mumsnet.com/learning/maths/grid-method-explained there are more steps than with the old method. I guess (unless you make a mistake) one advantage over the old method is that you don't have to remember to add zeroes beneath the sum when multiplying by ten or more. But, if you don't forget the zeroes, the old method is simpler and easier to sanity check.