Why do my HDCDs play lower on my HDCD machine?

I own two Arcam FMJ CD/DVD players.
My CD catalog includes many CDs that are HDCD coded which include artists such as The Grateful Dead, Mark Knopfler and Neil Young. I also own several HDCDs from the Audio Fidelity label.
My Arcam C36 is a CD player only with no HDCD capability.
My Arcam DV139 is a universal machine with HDCD capability.
My HDCDs play lower on my DV139 than they do on my C36.
Is there something wrong with either of my machines or are HDCDs expected to play lower on HDCD capable machines?
Or, is this the design of the Arcam machines?
I, one, cannot say I came across such a behavior and I don't believe is intended as such. Every time my CD player at the time played HDCD, the level didn't drop.
Thus I dare suspect that there might be something a bit wrong with the HDCD decoder on your machine...
Does this occur with both regular CD's and HDCD's, or only HDCD's? If it happens with both, then it is likely because the two CD players have different output voltages. I have a DAC that has a dramatically different output voltage than a CD player I have, so going from one to the other requires a volume change on the preamp.

Just a thought.

I have had that happen with my Naim CDX2. I think that some CD's are not compressed and "volume enhanced", my SACD
s usually play a bit lower in volume, my few anoying pop cd's play loud, this is often done to make a big initial impact. I am not sure there is anything wrong with your CDP.
Just turn it up and be happy! probably just output voltage difference or a difference in interconnects.
By default if it is going to have extended dynamics, the initial loudness must be lower to avoid clipping.

That may not be issue here, but my first guess.
One of the side effects of HDCD encoding is increased level when played on redbook CDPs. Playing HDCDs on HDCD capable players brings the level back to normal. Your Arcams are functioning as intended.
It depends on whether the HDCD recording uses Peak Extend.

[[When any HDCD Process Decoder recognizes an HDCD Peak Extended recording, it reduces the decoded average signal level of this recording only, to allow for the increased head room of the “extra” 6dB of dynamic range. For the other cases - HDCD recordings without Peak Extend, or non-HDCD recordings - the average decoded levels need to be matched to the decoded HDCD Peak Extended recording. This 6dB gain matching could have been built into the HDCD decoder, and done digitally, automatically, however we have given the user the option of doing the gain matching in the analog domain, which may offer some sonic benefits.]]