Nitpick: the galaxy in question is actually M33, or Triangulum, up to 3 million ly away (although Data's 2.7 million ly is an acceptable estimate as well, since the E-D was only said to have ended "on the far side" of M33, not necessarily meaning "through M33 and out the other side"). M22 would be a globular cluster within the Milky Way, just 10,000 ly away. So Picard is actually facing a journey just 38.5 times longer than Janeway.
In both the TNG episode and the VOY pilot, a central issue is that the distance would take X years to span "even at maximum velocity". In both cases, it is implied that it would be impossible to travel at maximum velocity in practice. We never get a clear quote for what the theoretical maximum velocity of the E-D or the Voyager
might be, only conjectural datapoints about "cruise velocity" or "redline".
So Picard facing a travel time 4.2 times longer for a distance 38.5 times longer is by no means a major discrepancy. Perhaps the theoretical top speed of Picard's ship is simply nine times higher than Janeway's?
As for subspace message travel time, there's something fishy about that "51 years" thing to start with. It's not really 51 years - it's "51 years, 10 months, 19 weeks, 16 days -" which defies conventional logic because 19 weeks is longer than a month and 16 days is longer than a week. So it very much sounds as if Data is listing a range of possibilities: "51 years for condition X, 10 months for condition Y, 19 weeks for condition Z, 16 days for condition-" before Picard cuts him off in disgust. And since Picard indeed does that, it may well be that none
of the conditions could ever be met in practice. VOY makes it pretty clear that subspace messages just plain don't carry all that far.
(Or perhaps they do travel across millions of ly - but only if there aren't galaxies and stars in between to disrupt the subspace landscape?)