I saw this as someone who's sparred with junior olympic bronze'rs, C-ranked fencer's, and someone who was literally a point away from being on the olympic team. They're great athletes, but it's a highly anemic skill set. Once I moved to kali and arma, I continued to use many *Attributes* of fencing, but almost none of the *skills*.
Here's the thing:
The HEMA community is fairly small, but very diverse. That means that there are some very serious & skilled people out there & some very stupid people out there.
YouTube - ARMA Senior-Free Scholar Prize Playing 2007
It's worth noting that not all of the people in that video are still affiliated with ARMA. ARMA is good but not the only good choice.
The very, very, very, Bad:
YouTube - Medieval Wrestling: Training Blindfolded
So, you have to be on your guard for Bullshido if you're getting into HEMA.
Sport fencing, on the other hand, is a competitive sport & so does a decent job of self-regulating quality within its ruleset. You'll be less likely to find a coach who's utterly bullshit.
Sport fencing is a wonderful & entertaining sport. It's also as combative as ping pong. The rules & weapons are too far divorced from real fighting to directly relate to fighting & you'll learn any number of habits that would get you into trouble with real swords. As has already been said epee is the least at fault in this, but it's still not my cup of tea.
In the final analysis: you'll never have to fight for your life with a real sword, so whatever you do is going to be a kind of a larp. If you're looking for a fun sport: go with fencing. If you're looking at fencing because you're interested in swords then understand: fencing does not use swords. If you like swords & that's your motivation or if you really want to know how people historically fought with swords & gain some perspective on that then try HEMA.
To those saying epee, I say saber - you get points slashing.
Yes, there are a huge variety of pistol grips and most fencers transfer from the French grip to one of the pistols fairly early in their careers. Pistol allows for more control, and it allows for an easier "flick" - that's where you snap your hand so that the really bendy blade bends big time allowing the tip of the (usually) foil to touch your opponent's shoulder or head, taking the blow out of the straight line defense.
There's the whole concept of priority in foil and saber that is an interesting study.
I've never done a two handed sword shtick.
Fencing has benefited my judo by focusing on flexibility (those lunges are killer), helping me with a better understanding of distance, and helping me to find openings. Fencing kit is much lighter than judo kit, but you have to get used to the helmet. Keeping your non sword hand out of the way is always interesting. When you go electric, you have to put up with that slight tug on the back of your jacket.
Fencing is fun. It's very cerebral. Given the strip, it really condenses the fight.
The sabre is the only sport fencing weapon that gives points for the cut. The problem is that there's no distinction between edge & flat on a sabre in terms of points. A hit with the flat wins just as much as a hit with the edge. Hard parries edge to edge are encouraged which is a terrible idea with real swords & only practical with ultra light/fast "weapons", such as those used in sport fencing, because it brings your weapon off-line from most attacks & so creates the parry riposte rhythm of the sport instead of encouraging actions in single time.
Also, the sport sabre is the most dramatic departure from its historical counterpart in terms of weight & balance. The speed & form with which you cut in sport fencing simply doesn't work with real swords & while thrusts can be fairly solid in epee & foil, there is no meaningful power generation in sabre cuts.
I'd advice you to try both a couple of times and hear what both are really about and see which fits you. Judging clips on the internet and trying to compare them is a bit dangerous. I know the two fencers in the first Hema clip and they had had about eight months of training at the time. I have no idea about the sports fencers, but I wouldn't be surprised if they had a bit more practice.
Timing and distance is VERY important, if not even more important in the Liechtenauer tradition where you make displacing attacks and try to circle the enemy. With spears, distance is even more important, since the reach varies with grip.
Also, you will get the opportunity to wrestle (ringen), use dagger, sword and buckler, sabre, rapier, grosse messer (big f-ing knife), longsword, spear, quarterstaff, halberd, war hammers and generally try to hurt your opponent in any way you can... A longsword fight can easily end on the ground with daggers, arm locks and choking. From a martial arts perspectice I think it is more proof than classical fencing.
I have great respect for sports fencers, but the main problem from a MA perspective, that is often seen, is a tendency to take hits as long as one hits first. This is common in Hema too, but something we try to work on.
Hema is still young and thus we have few real stars. Few have practiced more than five years, but of those who have had more practice, some are really good. The guys in the mentioned clip have also gotten a lot better. One of the guys can be seen here:
YouTube - David&Robert090201
Still, both of these have had only two years of practice.
You can find clubs and historical fighting manuals at my site hroarr.com Talk to your nearest club and see what it is all about.
Everything you are saying is true however I once spoke with a historical fencer (who also was a sport fencer) who told me a story about having a match with a sport sabre fencer using blunted basket hilt swords tipped and edged with rubber and wearing proper leather jerkins gorges and other safety equipment.
The sport sabre fencer went back to his instincts and training and flew at the guy and hit him with the blunted instrument breaking his collar bone.
The point being while sport fencing is devoid from true sword fighting the athleticism, timing and speed it develops is fairly deadly.
There was a DBM / kali person once on a thread here who described sabre fencers trying out the escrima stuff and their ability to "levitate and fly at you"
If someone where to want to develop a truly effective combat sword curriculum it would mix sport fencing training and historical fencing training. One to build the speed, skill and reflexes the other for the more deadly less easy to practice martial stuff.
Of course there's not much point.