Just some quick thoughts right before shabbos....
The gemara says that one cannot be mekadesh a woman with chalifin. Rashi explains by making 2 statements: 1. The reason less than a peruta doesn't work as kidushei kesef is because it is degrading to her. 2. Since chalifin by definition does not have to be worth a peruta, it doesn't work to be mekadesh an isha even when it is worth a peruta.
Regarding #1, Tosafos disagrees and explains that less than a peruta does not qualify as "kesef", and is therefore not included in the gezeira shava from where we learn that kesef works for kiddushin. There seems to be a dispute between Rashi and Tosafos as to whether less than a peruta qualifies as "kesef".
Regarding #2, Tosafos explains that the whole gemara is addressing chalifin that is worth a peruta. Originally the gemara thought that chalifin that is worth a peruta is similar enough to kesef to work as kesef, but rejects this and says that it is a seperate kinyan which we have no source for by kiddushin. Rashi and Tosafos would therefore argue if it were possible to entertain that chalifin would work when it was worth less than a peruta. Rashi holds that it was a possibility for chalifin to work even though it is a seperate kinyan from kesef, whereas Tosafos holds that we only thought it could work when it would be similar to kesef. I would like to suggest that perhaps their machlokes revolves around the definition of kidushei kesef. Is it a ma'aseh kinyan (like chazaka) or is it a reimbursement for which her receives the woman as a wife in return? Chalifin is clearly a ma'aseh kinyan from the fact that it can work when it is less than a peruta. Rashi holds that kesef is also just a ma'aseh kinyan, and therefore would be similar to kesef even though it is not worth a peruta. But Tosafos understands that Kesef is a reimbursement type kinyan, so chalifin which is just a ma'aseh that results in a kinyan would not be comparable to it at all.
There seems to also be a machlokes rashi and tosafos whether shtar that is more than a peruta, but for whatever reason an invalid shtar, would work as kidushei kesef. Rashi on the mishna implies it would (since he makes the case of kidushei shtar to be when it is less than a peruta, implying that if it were more than a peruta it would work as kesef), whereas Tosafos d.h. v'isha, implies that it would not (Tosafos says that chalifin worth a peruta should work, even if shtar would not work when worth a peruta. The reason shtar would not work is because it can be written on issurei han'ah implying that it doesn't need any value at all, whereas chalifin at least needs some value. This indicates that chalifin is still associated with the value of the object, and therefore when it has a peruta it should work like kesef).
If Rashi holds that shtar worth a peruta would work as kesef, why would chalifin worth a peruta not work as kesef? Perhaps rashi means to say that the Rabbonon were mevatel Toras Chalifin even when worth a peruta when it should work as kesef, so that you would not come to use chalifin when it is worth less than a peruta. But Shtar can work as kesef if it is passul when it is worth a peruta, because since normally it works less than a peruta chazal had no reason to uproot it from working as kesef.