Like others, I do think the comparison isn't perfectly apt. The Sward of Light are political units, recruited for both skill and loyalty (some units more than others), while Warrior Houses are composed of troops raised from youth and indoctrinated and trained in their house's ways. Sward of Light units are strengthened regiments with strong supporting forces, Warrior Houses are battalions with supporting infantry. And, within each order there are differences. Perhaps the Dai Da Chis might be a match for the Pillar of Steel man for man, the two more martial on each side. Maybe the more political Imuras match up better with the 1st Sward (in some periods, and other units in other periods).
But, by the by I do think the Capellan Lancers are a better fit. They two are recruited from a mix of the best of the best and the connected of the connected. Until Theodore, the 2nd Sward was the best unit in the Combine (perhaps the Inner Sphere) and the Red Lancers are usually the best unit in the Confederation (sometimes challenged by a really good Warrior House, since they don't pull from the same pool of recruits). Both are regimental sized with strong supporting forces. I'd imagine in a fight, they'd beat the hell out of each other pretty well.
For other houses...
The Knights of the Inner Sphere are perhaps closest to both. They're a philosophical order, like the Warrior Houses, with strong devotion to their ideals, but recruited as adults. And they take a personal oath to Thomas Marik, unlike most other FWL units, who's loyalty is to their home state, or perhaps to the League as a whole, or to someone else some of the time. They're a prestige unit, like the Sward of Light units and the Lancers to a degree, with plenty of shiny paint and smart uniforms, but they also happen to be elite warriors able to stand toe to toe with the best in the Inner Sphere.
The Davion Guards are broadly similar to the Sward of Light, but perhaps more egalitarian. They too are the presage unit with the fancy uniforms, and they too get a large share of the best troops. Doctrinally, they have less of a 'warrior' culture (though not none) and are a lot more at peace with combined arms and progressive tactics, unlike the highly militarily conservative Sward of Light (the Lancers are pretty tactically progressive, but with less of a combined arms focus; some Warrior Houses are super progressive, some not).
As for the Lyrans, the Royal Guards are the political unit, no question. Sometimes, they also get good troops. They always get the best uniforms and the most coats of paint, and they nearly always put loyalty above all else. But, the Sward and the Lancers and the Davion Guards nearly always have a unit or two (sometimes more) that are among the best in their nation, the military spearhead. The Royal Guards haven't tended to have a unit that serves that role, though post Jihad they've seen a lot more combat (in part because Tharkad is constantly under threat) and so have seen more use as premier units.
