Connecting a sub which way to go

In my experience, high passed small speakers/monitors with subwoofer setup is preferable, the speakers can play louder and cleaner, the power amps also don't have to work as hard as full range.
since you have everything on hand, why not try both way and let your ears make the decision, BTW, what is Paradigm S3 V2?

Paul McGowan (PS Audio) syas to use speaker cable from your amp to the sub. I scratched my head why speaker cables (main amp binding posts) to a powered sub, but it was a nice improvement 

However, I now have an Audio Alchemy DPA-1 (class D) AA says NOT to connect via binding posts, so.... check with the mfg

I prefer using the high pass option. I have tried both and I find that using the high pass give my mains a cleaner sound. Like the above post states,try both and let your ears you know which sounds better!

I am using both methods.
Main system has Vandy Treo's and 2wq subs using the Vandy Crossover.
Office has the VLR's and a pair of Hsu subs running off the speaker connections.
I like my Main system best, but the Office is no slouch. I might put in the HSU crossover, but I don't seem to need it right now.
Albeit, the Office has a bit more bass, but I kind of like the difference between the two systems.
As others posted, using the crossover relieves your amp from the heavy lifting of the bass frequencies, so if you are not using a very powerful amp, it might be the better of the two ways to go.
If you have a lot of headroom power-wise, it might not matter.
Bob

Ha! I came here to give you Paul McGowen’s answer: use a high level input for the sub. I appreciate the logic of it: whatever colorations or sonic signature your amp applies to the signal will also be applied to the sub and the speakers and sub will blend better.