Who is the king of Tube amplification between these two brands?
Bought my ARC LS15 and VAC amp back in 1995 and they are still going strong
Only service was cap upgrade on the LS15 
and just replaced the tubes in both just recently 
I had some experiences with both ARC and VTL entry amps 30 years or more ago. My system was ARC LS2, Adcom 555II, Luxman D-105u and Definitive Tech BP20 and Disco and electronic also my preference beside jazz.

ARC dealer let me take the classic 60 for home audition with no deposit needed since I visit that store often and got to know folks there. VTL needed me to purchase the Stingray but said I can return if I am not satisfy for any reason. 

The first generation Stingray looked cool and VTL is not for from my house. David Manley was cool and took time to explain on his VTL amp. I was very impressed with VTL top end tube gears but the Stingray sounded too solid state and harsh on the top end in my system. It was not very present exchange when I returned the Stingray. To but it mildly, it was unprofessional and I have not think of buying any VTL amp even now even VTL sounded more tube like than ARC tube amp. VTL has more classic tube sound and ARC is more detail and analytical but not harsh nor unpleasant on both of their higher end tube gears back then.

The Classic 60 was good but it didn't satisfy my need for Disco type of music.

I still own the LS2, changed the 6922 a couple times. Some statics when I turn on the volume up but the trick of put unit in mute and rotate the volume knob solve that issue. I would need to do that every few months.
I've owned VTL product for 20 years and have had nothing but Top Notch service from them. 
I have always liked the AR chassis. Cool and solid.

About Lyra cartridges, I feel very fortunate to have an Atlas SL.
Unbelievable upgrade from my Myajima Shalabi.
For sonic performance, every experience I’ve had is that VTL blows ARC out of the water. One of the top 3 systems I’ve ever heard was fully powered by VTL into Stenheim Alumine 5 at the Chicago show a couple years ago. Redefined what HiFi could be (but mostly a result of those speakers tbh).