Neck-through vs bolt-on and the bridge are, in my experience, somewhere near the bottom of the list of most important things about the bass. Far and away, how it sounds, does it stay in tune and does it break your arms when you play it and hurt your back, etc. are much more important features. You can go totally wrong or right or anywhere in between with a neck through or a bolt on. And no matter what bridge it has on it.
I've owned a number of both and once its slung over the leg and I'm playing it, the construction and bridge are basically out of sight/out of mind.
I can't really think of any advantages of neck-through other than it's easier to sculpt the neck heel area for comfortable access to the higher fingerboard area. There's no neck/body joint and screws, etc., so the neck-through is usually really comfy up there. The other item is appearance - neck throughs are really pretty.
The only other item is the neck cannot move whatsoever, due to sloppy joints or loose screws, etc.
That's about it as far as advantages. Everything else is disadvantages.
Think the reverse for bolt-ons. The main disadvantage of bolt-on being chunky construction at the neck/body joint and the additional machinery of a neck/body joint and screws, backplates etc.
I won't go into the debate about any differences in tone (there are none is all I'll say).
Basically, it's a pick your poison type of choice. Either one will be great if it's a bass that sounds good and you enjoy playing it.
As for the high mass bridge, some folks believe it helps sustain and gives some improvements to the tone. There is something to be said for a very solid connection of the bridge to the body; eg. the G&L bridge which has a connection as strong as the wood itself if not stronger.
Personally, I don't find that it matters much. There aren't a lot of bad bridges on basses these days so again this isn't something to lose much sleep over...
L