If you're talking travel, I wouldn't choose either of those lenses IMO. Why? Because they are heavy, and thats no fun on a long day of walking with a camera around your neck, or even in your bag. If you want the 300mm range with a lighter body while still retaining the optical and build quality of the L lenses, you should look at the EF 70-300L - its light (not crazy light, but significantly lighter than the two lenses you mentioned), and compact so its surprisingly comfortable to hold. That, or one of the 70-200 f/4's (IS or non-IS) as those are also significantly lighter than the 2.8 and the 28-300L - which according to the-digital-picture, falls into the heavyweight class.
That, and the 70-300L or 70-200 f/4 are cost quite a bit less than the two you mentioned. Both have IQ/sharpness on par with the 70-200 2.8's easily (I've owned both the 2.8 II, and sold it for the 70-300L) - so you get to save money too
The only downside to the 70-300L or even the 70-200 f/4 is that if you know you will be shooting indoors, or in weak light, they will struggle. That said, the 2.8 could struggle also, but is better suited to lower-light shots. If you are bringing the 16-35, then you are pretty well covered for indoor low-light shots already.