A few people in my playgroup seem to think that the Restriction on the City of Shadows Agenda works much like Seige of Winterfell.

In that, if your challenge is unopposed and you have no cards in shadow it will stop you from claiming all power that challenge (not only unopposed, but opposing titles, superior claim, etc... And since it does not state "for your house card" like seige, this would apply to renown as well)

Personally, I believe the difference is that Seige uses the word "During". Whereas CoS does not, and thus must be referring to only the single power you would gain for being unopposed.

So! who's right?

I believe you are correct. You do not claim power for unopposed challenges, but that shouldn't prevent you from claiming power for renown during an unopposed challenge.

Siege reads: "You cannot claim power for your House except during a MIL [challenge]."

City of Shadows reads: "If you do not have any cards in Shadows, you cannot claim power for unopposed challenges."

The key difference, really, is that Siege says "you cannot claim power" while CoS says "you cannot claim power for unopposed." In short, Siege is general (no power period) and CoS is specific (no power for a single thing).

Essentially, it's the same thing as always. If the card doesn't tell you directly to do it, don't go making crap up. City of Shadows is very specific that you do not collect power for a particular trigger that would normally award power. Siege takes the general position that you cannot collect power for any trigger that takes place within a particular timeframe. They really are not remotely equivalent because of the specificity of CoS.

Saturnine's observation that the word "during" in Siege is key speaks to the same point. Using "during" in conjunction with the blanket "cannot claim power" speaks to the general, "all triggers," nature of Siege while use of the word "for" instead of "during" in CoS speaks to the application of "no power" to the single, specific trigger (winning an unopposed challenge) instead of something general.

Another way to look at it is this: Let's say I have no cards in Shadows and during a challenge, I played a particular event that claimed power for my House. No problem. But at that point, I don't know if the challenge will be unopposed or not. When I get to challenge resolution and it turns out to be unopposed, does that make the previous effect claiming power illegal? Do I have to give the power back? If I do, do I get to take the event out of the discard pile and put it back into my hand? Lots of paradox here, so it's pretty clear that a "during an unopposed challenge" limitation is not a realistic thing to be assuming - or stating on a card.