One way of comparing this is hours played per day. I know that I got about 2.5k hours in a year and a half when I played actively. This comes to 4.5 hours a day on average.
This is probably pretty high for the scene, but it will naturally vary from player to player and over different time periods.
I'd say that, at least at some point, there were a lot of players playing 4 or more hours per day. That number probably isn't as high as it was but I'd guess there are still 60+ players playing at least four a day on average.
Korean Starcraft 2 players, at the very very top would play for 10-11 hours at their peak, while the average Korean Starcraft 2 player would play for 7-8 hours, compared to the average non-Korean pro playing for 2-8, with an average of around 5 probably.
I'm guessing that the MOBAs are probably similar to SC2, with 6-8 probably being about normal, with higher hours for Chinese players but a more consistent number globally. That's speculation. What you have driving practice in MOBAs is the fact that you can't guarantee what hero you pick and therefore need to be prepared to play a number, with all kinds of items and combinations and matchups to remember and consider.
Not sure how many hours CS:GO players play. Some googling suggests top players are playing 8-10 hours but I suspect this is exaggeration, since like Warband, there isn't as much to rehearse and memorise as in other games and most of the training will go into staying in shape as a player, covering all the important essentials of the game's mechanics. However, I may be wrong, since as a team game, there is a lot to be gained from familiarisation with teammates and learning to coordinate with specific individuals.
Overall, I think there are just a smaller number of Warband players playing with the kind of dedication you need to compete in other games. Hours played would probably have to be multiplied by 1.5-2 in most cases and teams would need to do a better job of playing together.
If Warband was played at that level, I think what we'd see is probably similar to the highest level of play now but a lot more consistent. There would be a greater number of headshots as extra time dedicated would allow for shooting to be more reliable and accurate (think Menethil at his best but a bunch of players like him, in every team).
Cav teamwork has advanced loads in the past year and can see that being taken even further, really polishing the timing of knockdowns followed by couched lanced hits for cheap kills. Naturally bumplancing and bumpslashing would be hitting higher success rates resulting in more smashed keyboards...
It's hard to say what would happen to Infantry. I want to believe that two handers would have a role in some kind of insanely pushed meta but realistically, I think people are pretty much there with gear setups. Perhaps we'd see a little more of the craziness that players like BlackTide and Technoviking demonstrate in their style but somehow slightly better understood and refined, in a way that would enable other players to learn and emulate the style. Rest assured, there would be a lot more players throwing javs like Cristo.
In terms of tactics, I think there is a lot of room for improvement. I see teams set into approaches that simply don't work, leading to whitewash sets, even now and even at the top level. Teams need to be able to switch their class setups more frequently and I think by playing more, with more high level opponents, teams would grow comfortable with making these big decisions with confidence. This could actually lead to a requirement for more players at the top level to be better at multiclassing. Perhaps a competitive Mount & Blade scene would expect players to practice a minimum of two out of three classes, increasing the need for practice time.
In answer to "how big is the skill gap?", I'm not really sure how to quantify that beyond what I've posted about hours spent. My thinking is that to be one of the top players, you'd need to spent about 600-1000 hours of good quality practice in Warband (I've heard this disputed) and I'd pitch other games higher than this by around 2-3 times.