"Very" different? "VERY"? Lets be serious.
xy1 = [1.43155281315397 0.00255865851191916
1.35675838019809 0.0145131910703132
1.27925136527898 0.063166446949049
1.19895069245412 0.210990679450789
1.1157710244529 0.540955972655767
1.02962188546981 1.06472307447546
0.940406331363923 1.60888586350091
0.848018802346465 1.86658100394464
0.752341384965735 1.66264882670706
0.653236684654374 1.13700864870653
0.550532598338051 0.596885427112396
0.443984551996628 0.240497869152622
0.333159864072945 0.0743572051584443
0.216939570864193 0.0176351499842711
0.0888515203255917 0.00320643723615615];
a1 = trapz(flip(xy1(:,1)),flip(xy1(:,2)))
xy2 = [1.3574514696438 0.00230062694421278
1.29605548980418 0.0132435702443471
1.23099970732201 0.0584912051989921
1.16214843460327 0.198236594379449
1.08935954807805 0.51564908418259
1.01248347607602 1.02957271312853
0.931361701492302 1.57808683823824
0.84582439298594 1.85693323865362
0.75568634779567 1.67746620095548
0.660739348290927 1.16327656092461
0.560735966899023 0.619215364238612
0.455349613170889 0.252967924578314
0.344052551344047 0.0792989196684651
0.22559115331588 0.0190697822153908
0.0930728988402219 0.00351835370743469];
a2 = trapz(flip(xy2(:,1)),flip(xy2(:,2)))
The difference is roughly 6.5%
100*(a1 - a2)/a1
plot(xy1(:,1),xy1(:,2),'r-',xy2(:,1),xy2(:,2),'b-')
So around 6.5% difference in area. Why should that surprise you? This has nothing to do with the use of trapz. The two have a different area, and trapz tells you that.
