I never fought in the SCA but did somewhat similar stick fighting for many years. The key difference was that we fought full force, full contact, "no holds barred" and used much less in the way of armor.
I have fought three escrima / arnis practitioners now and I was able to beat them about 9 bouts out of ten when they used their escrima sticks. They did a bit better when using my swords, but I still won. You can see part of one match from earlier this year here (he's only using one stick here but he tried two sticks first).
http://bellsouthpwp.net/d/e/deodand23/henry1.mpeg I went through a perod where I was fighting anyone who would show up to a fight, and have faced SCA fighters, staff fighters, sport fencers, kendo fighters and all sorts of generic psychos.
I know it is very popular these days but my experience with escrima is that basically no form of EMA can deal with a large shield or even a small one as in that clip. The escrima sticks are too small, and they only seem to have one guard to work from. It's easy to strike their legs for example. I see it as more of an augmented unarmed combat thing than a weapon technique.
Most SCA fighters suffer from the obvious deficiency of their sport- they don't know how to protect the "forbidden" strike zones. Some of the hard core ones however are quite good, I wouldn't utterly dismiss them all in terms of pure skill.
But I will say this, the only pepole I ever fought with weapons who were truly daunting were ARMA trained fighters. I was able to hold my own with the shield, but longsword v. longsword against jake was like being a candle flame in a hurricane. I never had that much trouble with any opponent before.
Since doing some WMA training I've been able to defeat spears and staffs with the longsword, something I could never do in the old days.
DB