Paul, several posters have given good feedback, but some may have missed points that may be important to you.

You mention not being pleased with the performance of your "does it all" lens. Well, if you are committed to using only one lens, even the best of these will negate most of the benefits of going FF vs. APS-C unless you don't mind bulk and especially weight.

You could probably improve image quality by sticking to a zoom with more limited range. It used to be a rule of thumb that going past 3:1 in focal length range was a sure way to degrade optical performance. Things have improved since those days, but there comes a point where pushing the range makes the optical design more difficult and costly.

If I were you, I would look at some of the offerings in smaller crop frame DSLRs, micro 4/3 and other mirrorless cameras. You might even see if you can rent from one of the on line rental sites or borrow from an acquaintance.

In my own situation, I am taking a trip to Alaska and plan to take a 12-24, 18-55, and 50-300 all in a small backpack. I realize this is a lot and would not be the best is a city environment, but I don't want to miss the opportunities for both scenics and wildlife.

I apologize in advance for the lengthy introduction. This is my first post here, but I have looked at posts and other places on the net for my questions.
I am looking for one camera for traveling, with one lens. Hand held, no tripod. Walk around camera, which generally I will have with me at all times.

1. I do not take portraits, nor do I go birding.
2. I travel for, and take photos of:
a. Landscapes, scenery.
b. Cityscapes.
c. Street scenes.
d. People going about their daily lives (not portraits).
e. Local street markets.
f. Gardens and flowers (My wife generally takes the macro close-ups with her camera).
g. Interesting buildings, architecture, and historical sites.
h. Inside of buildings, museum artifacts, and historical sites, when of interest.
i. Festivals, folk shows, performances, and parades.
3. I would not base my choice of camera body or lens on these:
a. Some video (e.g. of performances or folk parades).
b. A few wildlife photos or videos.
c. Very few sports/action photos.
4. See http://vacations-pm.blogspot.com for examples. I would look at the China 2009 photos and then perhaps the Europe 2012 photos.

I had a Canon XTI (original version), with one wide angle zoom and one telephoto zoom, but then went with the Tamron 18-270 so I only had one lens. Those photos seemed not as sharp as I would like. I want to upgrade the body in any case, and I dropped the camera and lens, and they would need repair. So it is a perfect time to look for new body and new lens. I am not limited to one manufacturer.

I would like as good as image quality as I can get, given the limitations of using a large range zoom. I was thinking of cropped 18 – 200 or full frame 28 to 300.

In reading about full frame and its better image quality, articles say full frame is good for landscape. But from the above list, we take pictures of a lot more than landscape. And other articles I read indicated cropped was better for landscape because of the depth of field.

I will probably have more questions, but for now my question is:

1. Do you think cropped or full frame would be better for me?

I'd recommend the 12-40 f2.8 pro on an EM-1 body, and put that resultant IQ up against just about anything.
Paul, look up on line a review by Ming Thein, an accomplished photographer: mingthein.com, or google EM-1 reviews, Ming Thein. Quite eye-opening, very well-written, and photo-specific and concise. I own both, a full-frame and a micro four-thirds, and the pictures I take with the EM-1 are every bit as professional as with my full frame. It is worth every penny of its $1300 price tag, and is gorgeously made. For your needs/uses, you'll be the envy of your friends and your wife will surely snag it from you every chance she gets. It'll change your life, and it is neither Dx nor Fx.

Hi Paul - travel, one lens, hand-held - look at the Fuji X-Series + 18-55mm f2.8-4.

Smaller than a DSLR, lighter in weight, less obtrusive in the street, APS-C Sensor, superb build quality, easy to use menu system, image quality as good as anything you can expect from a Canon/Nikon APS-C sensor camera, and ...... incredible low light performance.

X-E1 has great deals at present because it has been replaced (only just) by the X-E2, which has some improvements, but is more expensive. There are some excellent deals (until March 31st) on Fuji XF lenses and you might like to consider the 35mm f1.4 lens (great "street" lens) to add to the low light performance of the camera.

If you want to invest a little more look closely also at the newly announced XT1 which competes with the Olympus EM-1 mentioned above.

It's always good to explore your options BEFORE making your choice. Our role can only be to offer you options. Your job to do the follow-up research and decide !