A many-to-many relationship

Designing for maximum performance for an anticipated large user-base, I would suggest ensuring bookmarks and tags are not duplicated unnecessarily. Using my suggested schema below, http://google.com/ would become a single bookmark row. Users who want a bookmark to Google would have a row in UserBookmarksTags referencing the Bookmark row and the associated tag row.

I would tend to abstract the UserID away from the Bookmarks table, and use a cross-reference table to determine which users have bookmarks, and what they've tagged each bookmark with.

Using SQL Server, I would do it like this:

USE tempdb;
GO
CREATE TABLE Users
(
    UserID INT NOT NULL 
        CONSTRAINT PK_Users
        PRIMARY KEY CLUSTERED
        IDENTITY(1,1)
    , UserName varchar(255)
);
CREATE TABLE Bookmarks
(
    BookmarkID INT NOT NULL
        CONSTRAINT PK_Bookmarks
        PRIMARY KEY CLUSTERED
        IDENTITY(1,1)
    , BookmarkName varchar(255)
    , BookmarkURL varchar(255)
);
CREATE TABLE Tags
(
    TagID INT NOT NULL
        CONSTRAINT PK_Tags
        PRIMARY KEY CLUSTERED
        IDENTITY(1,1)
    , TagName varchar(255)
);

If every entry in your system requires both a bookmark and a tag, you could use the following table for maximum performance:

CREATE TABLE UsersBookmarksTags
(
    UserID INT NOT NULL
        CONSTRAINT FK_UsersBookmarksTags_UserID
        FOREIGN KEY REFERENCES Users(UserID)
    , TagID INT NOT NULL
        CONSTRAINT FK_UsersBookmarksTags_TagID
        FOREIGN KEY REFERENCES Tags(TagID)
    , BookmarkID INT NOT NULL
        CONSTRAINT FK_UsersBooksmarksTags_BookmarkID
        FOREIGN KEY REFERENCES Bookmarks(BookmarkID)
    , CONSTRAINT PK_UsersBookmarksTags
        PRIMARY KEY CLUSTERED 
        (UserID, TagID, BookmarkID)
);

The above version of the table UsersBookmarksTags allows you to quickly return a list of bookmarks for a specific user that matches any given tag, or all bookmarks for that user.

Alternately, you could create the cross reference table that allows null entries for both Tags and Bookmarks, as in:

CREATE TABLE UsersBookmarksTags
(
    UsersTagsBookmarksID INT NOT NULL
        CONSTRAINT PK_UsersBookmarksTags
        PRIMARY KEY CLUSTERED
        IDENTITY(1,1)
    , UserID INT NOT NULL
        CONSTRAINT FK_UserBookmarks_UserID
        FOREIGN KEY REFERENCES Users(UserID)
    , TagID INT NULL
        CONSTRAINT FK_UserBookmarks_TagID
        FOREIGN KEY REFERENCES Tags(TagID)
    , BookmarkID INT NULL
        CONSTRAINT FK_UserBooksmarks_BookmarkID
        FOREIGN KEY REFERENCES Bookmarks(BookmarkID)
);

This allows rows that have a bookmark without a tag, and also allows tags to be associated to a user without a bookmark.

If there is a requirement to know all the tags a user has added, without those tags necessarily having an associated bookmark, I would consider adding another table for that purpose, as:

CREATE TABLE UserTags
(
    UserID INT NOT NULL
        CONSTRAINT FK_UserTags_UserID
        FOREIGN KEY REFERENCES Users(UserID)
    , TagID INT NOT NULL
        CONSTRAINT FK_UserTags_TagID
        FOREIGN KEY REFERENCES Tags(TagID)
    , CONSTRAINT PK_UserTags
        PRIMARY KEY CLUSTERED 
        (UserID, TagID)
);

In your scenario, since (if I'm understanding correctly), every User will need to complete every Task in the Projects they belong to, there will need to be one UserTask per Task per User if you want to store things such as dateCompleted.

Because of this, Option A makes sense to me. You need to be "reacting to these events all the time and acting in response" anyway. One modification I would make though is that I would include a defaultHideOnComplete field in the User table. The TaskUser's hideOnComplete field would be initially set to the defaultHideOnComplete value for the User associated with it.

Option B doesn't make sense to me with what you're trying to accomplish, because it doesn't allow for every User to set their own hideOnComplete and priority values.

Let me know if I'm misunderstanding something : ]