The Minchas Chinuch has a paradoxical chiddush: Since every violation of a din derabbanan is a violation of both lo tasur and v'asisa al pi hadavar asher yorucha, it comes out that a din derabbanan is more chamur than a violation of a single lav d'oraysa (2 issurim vs. 1). Nafka minah: Where there is a choice between two prohibited foods, a choleh should always be given the less severe issur to eat -- ma'achilin lo ha'kal ha'kal techila. Given a choice between eating a food that is assur m'derabbanan and a food that is assur mdoraysa, the Minchas Chinuch suggests better choice would be to eat the food assur m'doraysa, as that would violate only a single lav instead of two.
The footnotes of the new Minchas Chinuch point you to a few places where R' Elchanan proves that the din d'oraysa is in fact more chamur. R' Noson Gestetner in his L'Horos Noson (the perusal of which makes for oneg Shabbos and which is available online here) explains why. The Rishonim discuss whether it would be better to shecht an animal on Shabbos to obtain kosher food or whether it would be better to feed a choleh neveilah. The Rosh writes that it is better to break Shabbos. Even though the punishment for breaking Shabbos is far more severe (misah) than the punishment for eating neveilah, the issur of Shabbos is extrinsic to the food itself - it's like a lion that blocks the way to a good meal. Neveilah, however, is like inedible, not merely inaccessible, food. Here too, issurei derabbanan are issurei gavra (see R' Yosef Engel in Esvan D'Oraysa who discusses this at length) that prevent access to the food. The issur Torah on the food taints the cheftza of the meal itself.
While the lomdus sounds nice, I don't understand what he means. The point of ma'achilin lo ha'kal ha'kal techila seems to me to be to minimize the issurim being done -- it's not a specific din in issurei achila, but is a more general concept: Don't be a big rasha when you can be a smaller one. What difference does it make if issurei derabbanan are issurei gavra or issurei cheftza -- bottom line remains that eating food assur mderabbanan entails violating two issurim while eating neveilah or some other food that is asur m'doraysa entails violating only one issur.
As for why violating Shabbos to obtain kosher food is less severe than eating neveilah, I seem to recall a Netziv which explains that issurei achilah have the added downside of corrupting the neshoma in a way other issurim (even with more severe punishments) do not. Those learning daf yomi may recall from early in Chulin that Hashem does not allow tzadikim to even inadvertently violate issurim. Tosfos holds that this special promise applies only to issureiachila, not to all cases. This underscores the special danger posed by foodstuff.