Skill definitely effects your ability to cut (cause damage with a sword). If you don't know what you are doing you can in some cases barely cause any damage at all, it's pretty easy to slap with the flat, to hit and pull back right away, to where you can't even cut a plastic water bottle (it will just fly away) or a pool noodle. On the other hand if you do know what you are doing, you can
Tatami are pretty hard to cut, and are used (at least today) to improve your cutting skill.
People lining up cuts in youtube videos are not particularly skilled at cutting (myself included) but they are starting to have more realistic cutting contests now in HEMA circles.
Here you can see Mike Edelson doing some Mastercuts on Tatami
and here some quicker ones
In Japanese and Korean martial arts circles that has been going on already for a long time and they have it down to a science, I think this is as fast as in any real fight.
Here is a fairly realistic test showing rate of shots for a longbow vs. a relatively low powered (about 180 lbs) crossbow. That is about the lowest grade for military use historically, most would be much stronger and as Spiryt said, require spanning devices.
These weapons were used in very different ways though. One of the many differences between them is that infantry crossbowmen were often deployed behind a pavise ('tower shield', more or less, in most RPG's) and two weapons were used, one being spanned by an assistant while the other was aimed by the shooter. The other way was mounted on horseback where they would shoot and move out of distance, more similar to the way pistols were used.
They were also used less often for 'area fire' for lack of a better word (bad term since bows aren't 'fired') though they were also used that way ... bows tended to be used more for 'lofted' shots and crossbows were more specialized at direct shots. The crossbow tends to have a much longer direct-shot range for individual targets, and is more accurate, but the longbow shoots a lot further at small areas (where the rate of shots is much more important)