Which integrated amp would you pick?

Neither one.

@georgelofi
Please stop advertising Parasound Halo.
Mediocre Integrated amplifier

I know you directed this at georgelofi, but I had to chime in.  No one is advertising Parasound, just stating facts and opinions.  Just because you do not care for them does not mean they aren't any good..  Yes, there are a lot of integrateds, but personally I wouldn't touch Class D with a ten foot pole and I have already had tube integrateds.  I prefer the JC designed solid state Parasound.

I don't know which Musical Fidelity you are speaking of. There is an M6500i and a M6si. Perhaps there was an M6 before this???
I have heard the M6500i. It is a dual mono design and it sounds truly amazing for an integrated amp. It will sound better than many mono amps paired with a preamp.
I have the Parasound A21 HALO amp and P3 preamp, which should not be that different than the new HALO integrated. This combo is as good as the MF, I think. I would listen to both the MF and the Parasound for comparison using your own ears.

Of course the speakers you will use should make a difference, but both amps have ample power. I would give the edge to the M6500i.

I have not heard the M6 but have owned the A3.2, A308, KW500, and NuVista 800. I really liked all of them. The KW500 was fantastic (still have it for when I put my second system in place). The NuVista 800 is truly world class in my opinion. However, I have not heard a Parasound amp for several years now--I did like it though I can't recall which model. I agree with 2psyop. Listen for yourself.  When I started out, I spent countless hours listening to LOTS of gear at several excellent local HiFi shops. I identified a sound that appealed to me and have built on that sound, following the mantra of "same but better," as I have changed gear. It has served me well. I love my system. If you have questions about MuFi, contact Randy Bingham (in charge of US sales). He is very helpful, knowledgeable, and a nice guy.