Honestly, they're just different. I never really heard much about USMLE from upperclassmen, but rumors about the COMLEX always centered around how vague and poorly-written the questions were. After taking them both, the COMLEX is less of a poorly-written test and instead is vague and tests concepts generally regarded as low-yield; I actually felt the questions were better written than I was anticipating. The USMLE is detail-oriented and tests mechanisms. I do personally feel that the USMLE is better written and is an overall better gauge of a second year medical student's knowledge.
USMLE:
It is more detailed than the COMLEX. The questions will give you all of the information necessary to make the correct diagnosis or may actually give you the diagnosis. For example, the USMLE may give you a few pertinent lab findings, an important historical fact, and two classic physical exam findings for a certain disease. Some of the questions will ask for a straight-up diagnosis, as there are plenty of first-order questions. The more difficult questions will then ask about the disease in a way you have never thought of or will attempt to make you think about the disease in a different context. In order to do well on USMLE you need to understand mechanisms and retain knowledge of details. It also stresses more biochemistry and molecular biology/genetics than COMLEX. The answer choices are also much different than the COMLEX. With USMLE, the answer choices are often very similar or worded in a strange manner such that it makes picking between two choices more difficult because they may essentially seem the exact same. Unless you really understand mechanisms or details it may be tough to get those "hinge" questions correct.
Bottom line for the USMLE: work on understanding mechanisms and, while studying, attempt to think about how (and why) certain disease process will affect other (seemingly unrelated) organ systems. Also don't forget about those esoteric details that may possibly show up (although rather rare).
COMLEX:
It is less detailed than USMLE and asks that you see the "big picture" (although seeing the big picture should be your goal for both exams). In my example above where the USMLE question gave you the lab findings, the historical fact and the two PE findings, the COMLEX may give you one historical fact and a single PE finding. As a result, you have to know the disease process very, very well in order to narrow down the answer choices. The answer choices also differ wildly from each other. In fact, many of the answer choices will be completely unrelated (again, this is in stark contrast to the USMLE answer choices). This is one of the reasons why many students say the COMLEX is so vague: they give you little data and answer choices are completely unrelated. It is possible, however, to get those questions correct if you really know the material well (seeing the "big picture") because you can so easily rule out the wrong answer choices. The questions asking about mechanisms or diseases in different contexts were pretty rare. There are still a good amount of first-order questions.
Bottom line for the COMLEX: work on understanding each disease in a larger scope and be comfortable differentiating between two diseases that present similarly (when only given a small amount of information). Also, be very comfortable with microbiology and organism classification. You can even go out on a limb and study the rare bugs if you have time.
How to study for both:
I personally feel that all you need to study (and do well) is First Aid, UWorld, and a pathology review source (Goljan RR [the source I used and my personal recommendation] or Pathoma). I felt very well-prepared for both exams while studying with these resources. I found USMLE to be more difficult (it has a few more 2nd- and 3rd-order questions) than COMLEX. I actually felt over-prepared for COMLEX using only the above three resources. The best thing you can do for yourself is study hard for your two preclinical years, as a strong foundation is the best resource of all. You will, of course, need to supplement your COMLEX studies with Savarese and a source for Chapman's points, but other than that, they both test the same material, just in a slightly different way.
I hope this gives you and future test takers a little insight in to the two exams. Feel free to PM me with any other questions.