Attack speed% on weapons only works for that weapon. +attacks per second works for both weapons. The +.19 attacks per second on the 1.4 speed sabre is already a 13.5% attack speed increase. Depending on your other weapon it would be somewhere around that as well.
While higher weapons could have more attack speed even if it only increases the weapon with the mod...it really depends on when those start showing up. Currently we could be looking for good superior weapons to level up with. Also what if the mod also increases with level on the superior weapons(seems doubtful because you could get ridiculous speeds)?
No, as far as I know every other weapon-specific bonus (any type of bonus weapon damage, procs or +x% attack speed, Life leech) applies only to the weapon on which it spawns. Damage from the primary stats always apply to both weapons of course.
I'm not sure about bonus crit chance, crit damage and on hit bonuses. Since Life leech is per weapon I assume on hit bonuses are the same.
How about for skills that don't rely on a specific weapon to be swung though? Do both weapons' bonuses apply to that skill? Because that would affect skill choices a lot, if the difference in modifiers is so grand.
Skills don't affect how modifiers are applied. For example, if you dual-wield two weapons with 10% bonus APS and a skill only uses your main hand weapon then the 10% bonus on your off hand won't suddenly apply to your main hand when you use that skill.
I'm going to derail the topic a bit here, in favor of curiosity.
Do most/all skills rely on only the MH wpn to calculate damage then? Or does it always alternate according to the last weapon swung before a skill goes off? Let's say Barbarian's Revenge is used - which damage modifiers from weapons (in the case of dual wielding) would be included in the skill's final damage? Or is it calculated from the Status Screen's listed dps?
Most skills I looked at alternated between my weapons, but we don't know exactly which skills alternate and which skills doesn't. It's not always trivial to test this, especially with channeled skills. We would need much larger differences in item level to get definitive results on this, larger differences than what the beta provides.
As for skill damage, everything is included from the weapons in the damage calculations, not just base damage as some people think for some reason.
For skills that scale with DPS, you can just multiply your listed DPS with the skill's damage multiplier and you'll get your skill's DPS. Of course things are more complicated than this in the "real world", because DoTs won't stack, AoE skills can hit multiple targets, etc., but you can use this method to get your single target DPS for most skills.
Calculating the damage of skills that don't scale with DPS takes more time, because you have add up all damage bonuses from your weapon and gear.
Can't you pick a beta top-end weapon and compare with the starting weapon? If you can get any results, it'd probably justify its own thread.
They really should list total damage and attack speed on the character screen (if they don't already, sorry I haven't looked at my stats much when I got the open beta, was too busy actually playing), and not just DPS.
For some skills that's not enough in the beta. For example hand crossbows are really fast, so their damage is low and there's only type in the beta. Testing DH skills like this is impossible. IIRC the character sheet alternated with every skill I've tried, but I don't trust it.