I like carrying everything in panniers, rather than a trailer. There's less weight, less rolling resistance, and no need to bring a different sized spare tube. However, your bike must have capacity to carry racks. There are adapters if you don't have braze-ons, but make sure your chainstays are long enough that your heels won't hit your rear panniers. Also, make sure your rear wheel is heavy-duty enough to carry the extra load. I've broken spokes on tour and it's a drag.

Bob trailers have the advantage of being narrow; the wheel follows the bike's wheels, which makes it easier to navigate through obstacles - rocks, tree branches, potholes, etc. I found mine to handle great. I never had a handling problem. However, there's a tendency to jackknife when handling off the bike - parking, loading, etc. This can put quite a strain on the stays, from what I've heard. Be careful and you'll be fine. Be careless and something could break.

I've never used one, but the Burly would seem to have the advantage of having almost all the weight of the trailer born by the trailer's wheels. There should be no jackknifing issue. The disadvantage would be the extra weight and the need to account for the wider footprint when navigating through obstacles.

If you're doing the west coast, I'd recommend north to south to take advantage of the prevailing winds. I'd also recommend July and August. My nephew started from Vancouver in late September and the weather was horrible. His experience was completely different than mine (last two weeks of June and first two of August - warm weather the whole time, and only two brief spells of rain - less than 24 hours each time.)