You have way more flexibility with all of Vergil's moves in DmC vs DMC3, the summoned swords, blistering swords, storm swords, and spiral swords are all independent, so you can have all three moves occur simultaneously. You do not need to first activate spiral swords in order to do the other moves.
The flush attack is similar in a way, because well it looks very similar, but no seriously, it is a projectile with no wind up time that can be fired endlessly and one that also embeds itself into the enemy. This is awesome because in new DmC, any embedded enemy can be demon pulled or angel pulled.
As for the wind up time, how can I stress this enough? there is really no wind up time, the way it works is that whatever enemy has an embedded sword, which can happen by either shooting swords, or simply attacking enemies with various attacks the game will automatically teleport you to them or them to you without any distance limit. You can be half across the level and still have this ability work. I only show it clearly to showcase what it does and how it works, while playing you'd be hard pressed to find any "downtime".
And I'm playing the PC version w/ turbo, even though DmC isn't with turbo, so now that I think about it that seems unfair. I should have increased DmC's in game speed by 20% as well, this is easy to do, I just don't like playing on Turbo in DmC.
To answer your question about certain moves being compared, I compared similar moves with their rough approximations, or moves with similar functions. If I went in more detail it would only highlight the limited move set of Vergil in DMC3 and the repetitive function of certain moves, hightime vs upper slash, its basically the same move, and downward slash also seems kinda weird.
And finally, may I add that all of new Vergil's moves can be cancelled at any time at any moment air or ground. That alone adds a huge bonus to his arsenal vs old Vergil. I just really would suggest you try out you new Vergil you'll be very happy with how his moveset has been upgraded and revamped in DmC.
Honestly, I think new Vergil's moveset is more suited for ninja gaiden than the old ones.