Why is LDL more easily oxidized/damaged than HDL?
Just a brief background about lipoproteins:

Lipids and proteins associate noncovalently to form lipoproteins, which function in the blood plasma as transport vehicles for triacylglycerols and cholesterol. Simple, unesterified fatty acids are merely bound to serum albumin and other proteins in blood plasma, but phospholipids, triacylglycerols, cholesterol, and cholesterol esters are all transported in the form of lipoproteins.

In general, lipoproteins are classified according to their densities. The densities are related to the relative amounts of lipid and protein in the complexes.  Thus, there are:


high-density lipoproteins (HDLs),
low-density lipoproteins (LDLs),
Intermediate density lipoproteins (IDLs), 
very-low-density lipoproteins (VLDLs), and also
chylomicrons. 


Chylomicrons have the lowest protein-to-lipid ratio and thus are the lowest-density lipoproteins. They are also the largest.



There are a couple of things to take into consideration:


How they function


LDL appears to be the major circulatory complex for cholesterol and cholesterol esters. At various target sites, particularly in the capillaries of muscle and adipose cells, these particles are degraded by lipoprotein lipase, which hydrolyses triacylglycerols. Lipase action causes progressive loss of triacylglycerol (and apoprotein) and makes the lipoproteins smaller. This process gradually converts VLDL particles to IDL and then LDL particles, which are either returned to the liver for reprocessing or redirected to adipose tissues.  This results in even more increase in LDL than other lipoproteins.


Environment


Another explanation is based on environment conditions -the LDL binds to specific LDL receptors, which cluster in domains of the plasma membrane which subsequently form coated vesicles which pinch off from the plasma membrane and form endosomes. In the low pH environment of the endosome, the LDL particles dissociate from their receptors. The endosomes then fuse with lysosomes, and the LDLs are degraded by lysosomal acid lipases into amino acids, fatty acids, and cholesterol.

Newly formed HDL contains virtually no cholesterol ester (however, over time, cholesterol esters are accumulated through the action of lecithin:cholesterol acyltransferase).

Another associated protein, cholesterol ester transfer protein, transfers some of these esters to VLDL and LDL. Alternatively, HDLs function to return cholesterol and cholesterol esters to the liver. This latter process apparently explains the correlation between high HDL levels and reduced risk of cardiovascular disease. High LDL levels, on the other hand, are correlated with an increased risk of coronary artery and cardiovascular disease.

Reference 

Biochemistry (Grisham)

Biochemistry (Campbell and Farrel)