We have an Assassination Rogue and a Dual-Wielding Champion Fighter in our party, and we often divide our items trying to maximize party damage output. One pattern that we have noticed is that any weapon that works for both characters is better suited for the Fighter. With his Extra Attack, the Fighter will always cause the weapon to do more damage than the Rogue (who has a single attack).

Currently, the Rogue has two +1 daggers, and the Fighter has a +1 shortsword and a regular shortsword. The Rogue was given both daggers just to ensure Sneak Attack could land as magical damage. They've not picked feats yet and will reach level 11 next week. Both have maxed out their Dexterity scores.

However, as more weapons are found now (Vorpal Swords, Sun blades, etc), it seems like the optimal strategy is to always give them to the Fighter first, and his 'leftovers' are then given to the Rogue. Since they will now both have 2 magical weapons, the Fighter is always the best choice, DPR-wise.

What kind of magical weapon (if any) is better suited for the Rogue rather than the Fighter?

Avoid Pure Damage

A magic weapon can do a lot of things other than buff your damage. A Weapon of Warning, for example, gives advantage on initiative rolls, and thus would be perfect for an assassin rogue. A Dagger of Blindsight (from Waterdeep: Dungeon of the Mad Mage) would be equally appropriate, allowing an Assassin to skulk around even in magical darkness.

Fighters get Extra Attack, and so they can leverage extra damage well. You need to find a way to leverage what you have (benefitting from going first, benefitting from advantage, et cetera).

A Weapon of Warning is a good fit for an Assassin Rogue.

A weapon of warning doesn't deal extra damage, but

While the weapon is on your person, you have advantage on initiative rolls. In addition, you and any of your companions within 30 ft of you can’t be surprised, except when incapacitated by something other than nonmagical sleep.

Advantage on initiative rolls is useful for an Assassin, since they get advantage on attack rolls against creatures that haven't taken a turn yet. And because the weapon doesn't have a damage bonus, the fighter won't get as much out of it.

Give Attack Bonus to Rogue First and Damage Bonus to Fighter First (With Many Caveats)

As others have well explained a weapon that generates advantage should basically always go to the Rogue first, because it radically increases their chance at sneak attack. However you will likely encounter a pile of other magic weapons along the way so I will not focus on this.

With most magic weapons the basic principle should be that, when sneak attack is available, it is more important that one of the Rogue's two attacks hit than that one more of the Champion Fighter's hit, and statistically it is more difficult for the Rogue to land a hit since they have fewer attacks. A level 11 Rogue with sneak attack will do an average of 21 extra damage from landing a sneak attack but even dual wielding and using their bonus action they will only get 2 bites at that apple. This sneak attack damage, when available, is on average the bulk of the damage they will do (especially since the offhand attack doesn't get their dex bonus, and this generally applies even if their weapons gets a damage bonus. Often they will not even get the offhand attack because of the many things they can and often should do with their bonus action.

Meanwhile the fighter will statistically have more attacks hit in their turn. Thus bonus weapon damage matters far more to the fighter than the Rogue. Consider also that the champion has an expanded crit range so they will double the damage dice of the extra damage twice as often. Consider that they will use the offhand attack a bit more often since they have fewer bonus action options.

Another factor is that for the level 11 Fighter three attacks can be with one weapon, one with the other which makes one sword of damage awesomeness more valuable than two swords of half as much damage awesomeness.

But, using an example of fairly typical magic weapons, I would say that a straight +2 weapon should probably go to the Rogue first whereas a +1 with 1d6 damage bonus should probably go to the Fighter first. The first is more likely to hit, the second does 2.5 more damage on average then the first when it does.

In terms of the offhand weapon the answer is clearer: favor the Rogue with anything that ups attack if they frequently use their bonus action to attack and the Fighter if they don't. The difference in what damage the weapon will add to the single bonus action attack for one character versus the other is marginal compared to a high level sneak attack happening or not happening.

I'm afraid because of these numerous variables, and the variability of enemy AC, it is exceptionally complex to actually calculate the permutations for average damage even of example scenarios with example weapons, particularly if a dual wielding character does not have identical weapons in each hand. (I started to do it, and it quickly involved about a page of calculations for each scenario. For example, there are eight different results for how many combinations of hits or non-hits a level 11 fighter with two different weapons can do and for each one there are permutations of how many crits v. non-crits, and then they can also action surge!). So, realistically, you'll just have to get a feel for whether a particular weapon is frequently making the difference in a Rogue hitting with sneak attack or not hitting at all.

Moving beyond actually optimizing party damage output, consider finally that, since the Rogue is statistically less likely to hit at least once with any weapon, that player, without a weapon increasing attack, is substantially more likely to have a complete bummer turn where they just miss and do no damage at all, and that makes for less enjoyable gameplay for most people.

Any weapon that deals burst damage, improves initiative, or grants Advantage

A solid example is the Oathbow.

The Oathbow is a ranged magical weapon, and has this text:

When you make a ranged Attack roll with this weapon against your sworn enemy, you have advantage on the roll. In addition, your target gains no benefit from cover, other than total cover, and you suffer no disadvantage due to long range. If the Attack hits, your sworn enemy takes an extra 3d6 piercing damage.

Additionally, regarding the Rogue's Sneak Attack feature:

Once per turn, you can deal an extra 1d6 damage to one creature you hit with an attack if you have advantage on the attack roll. The attack must use a finesse or ranged weapon.

Lastly, consider this from the Assassin Rogue Subclass:

You have advantage on attacks rolls against any creature that hasn't taken a turn in the combat yet. In addition, any hit you score against a creature that is surprised is a critical hit.

As a Rogue, you can gain your Sneak Attack damage bonus on any attack that has Advantage without having an ally adjacent to your target. Add that with the added range and guaranteed advantage of the Oathbow, as well as the fact that the Assassin features allow you to critically hit more often while applying the bonus damage of the Oathbow, and you have a highly effective weapon for any Assassin Rogue.