The Player was smoother/fatter sounding, bordering on muddy. The 40th had more going on in the mid-to-upper midrange, a growlier and slightly clankier/slimmer tone. I'm assuming you are using strings of the same type and more or less the same age. Still, these tonal differences are more or less the same as what I've been hearing when playing these two models (I own a Player, where I ended up replacing the pickup but I've only tested the 40th basses rather briefly).
My ideal tone would probably be somewhere between these two to be honest. I've always found the Players slightly too muddy sounding but I'm also personally not a huge fan of too much "middle-midrange" growl. As a reference, Lollar standard J-pickups are perfect for MY taste. But I probably use different strings and have a very different playing style so any comparisons are pointless really.
If I HAD to choose based on these clips, I would say the Player maybe had a tone that was slightly nicer for your style of playing. But I don't know what kind of tone you're aiming for. Smooth? The Players was better for smooth/fat. Growly? The 40th was better for that.
And I know what you mean about those 40th necks. They are VERY comfortable necks. I've personally never liked the neck profile on the Players. The "feel" of the neck is THE most important thing with a bass IMO so if the 40th feels nicer to YOU, you've DEFINITELY made the right choice.
Still, both basses sound great. We are discussing nuances here. You would get a much more significant difference in tone simply by changing to a different type of strings.
You can always replace the pickups at some point if needed, but other part of the bass will of course also affect the tone to some extent. I believe the 40th Anniv. basses have bodies made from nyatoh, which is supposed to have similar properties as mahogany. I don't have a lot of experience with nytoh, but I generally don't like mahogany for bass bodies, exactly because of a certain midrange character that isn't right for MY preferred tone. There are exceptions though and the differences between different body woods can be VERY subtle compared to say, a change to a different type of strings.