1. Correct size for the airlines you use. A lot of bags will say that they are "carry-on" or "airline approved" but you really need to check the requirements on the websites. In general I have found that a consistently acceptable size is 56 x 26 x 23 cm which is sometimes called 115cm linear. There is a great guide for Australian airline carry-on sizes on AusBT.
2. Durability - this one is hard to tell, but the most wear and tear on your bag will likely be the space between the wheels and of course the wheels, so a bag that has additional reinforcements in that area and solid, in-line skate wheels is usually your best bet. I have to say, I don't have any personal experience with the 4-wheel carry on but in general it seems 4-wheelers are for the occassional traveller. Check out Australian Business Traveller, Tripadvisor and surprisingly the Sydney Morning Herald for similar arguments on the 2-wheel vs 4-wheel saga. Possibly a post for another day here at Licorice & Olives?
3. Warranty - whilst going on a holiday and having your suitcase break is obviously not going to be the best situation, having a bag with at least a 5 year warranty is essential in the life of a suitcase.
4. Design and Flexibility - I previously had a carry-on that just had one handle, which is just fine for most people. However, as all good women do, I have my handbag full of terribly important things that I don't always want to carry over my shoulder. Often I want to rest the bag on the top of my suitcase. I quickly realised that you can't do that with a single handled suitcase. There is also less stability when you are going up and down footpaths and stairs but most people would probably just pick their bag up rather than bashing around buildings and streets.
Another design element to consider would be the internal space within the bag. Some bags have the option to extend the bag. You may not expect to use this but you will be surprised how often you end up using it. Given the option, you will not have to worry about buying a new jacket in Shanghia or throw rug in Melbourne. Of course, all that shopping would mean you would need to check your bag but its still good to have.
It is the Antler Aeon 51cm and it is just a great bag. You know it is good when there are at least 10-15 people with the same bag on each and every flight I take. It is a little smaller than the traditionally allowed 56cm size, it always fits perfectly in the overhead lockers and is sometimes a bit of a squeeze so I wouldn't want to go right up to the 56cm. One frustration? I purchased the green version before they brought out the more awesome orange colour.
Of course if all this fails and you are forced to check your bag, here is an interesting article over at the Air Travel Luggage Consultant Weblog it is a little old but it is a rather humerous read.
*I have no affiliation with Antler or any luggage company, I just really love this bag.