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What gives me a bigger chance of getting a rare out of a radshare? 1 by 1 or the whole squad in one go?



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Same chances.

If all 4 players equip the same relic, it's be like doing 4 runs in one go. So it's only faster.

Personally I'll mostly choose whole squad in one go. faster, and less things can go wrong when with randoms.

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The odds are the same, but as others have said, it does depend on how many you need (want) and if you can trust the others to execute the plan.  The odds breakdown are as follows:

Get at least 1 Rare: 34.4%
Get exactly 1 Rare: 29.2% 34.4% (Since you only get to pick 1 out of 4, getting 2, 3 or 4 Rares is the same as getting 1 Rare).
Get 2, 3 or 4 Rares: 0% (You only get to pick 1)

1 by 1 (each round, only 1 player carries the desired Radiant relic, the Rare below refers only to the Rare from that relic):
Get at least 1 Rare: 34.4%
Get exactly 1 Rare: 29.2%
Get exactly 2 Rares: 4.9%
Get exactly 3 Rares: 0.4%
Get exactly 4 Rares: 0.01%

So as you can see, if you just need 1 copy of the Rare reward and do not care about getting more than 1, then both methods are equivalent.  But if you would like to try your luck at getting more than 1 (for either ducats or selling to other players), then 1 by 1 is better.  However, the 1 by 1 method is 4 times longer and riskier as other players could bail on you so...

Finally, another consideration is how difficult the relic is to obtain.  If the relic is not vaulted and easily farmable, then you might as well just go with radshare.  If you don't get the rare drop, just go farm another one and come back for another radshare.  But if the relic is vaulted or otherwise difficult/costly to obtain, then you might want to consider 1 by 1 to make it possible to obtain multiple copies.

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Overall it's the same chance, but there are tradeoffs to each strategy.

If you run them one-by-one it obviously takes 4x as long, and you could more easily be scammed by strangers leaving early. However if you run them all at once, there's a chance that you roll two parts you want at once, and you're forced to basically waste a Relic. This isn't particularly likely, but it can be a real kick in the pants, especially if you're going to a part you need two of. It would also be much more likely if you're only going for an Uncommon part.

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