These seem to be similar baits.  Would you use the same rod for both if tossing similar weights?  Or do they call for different characteristics?  There are many suggestions and recommendations for rods to use for jigs, but I haven't found any for tubes.

Many (most?) usually don't get quite that specific - i.e. they'll get a "plastics" rod, vs. type of plastics as you describe. In your case, you'll be fine, unless you intend to go heavier on the jigs - i.e. more than 1/2 oz - then it depends on how heavy or light action of a rod you are considering.  Typically when fishing tubes it's not with a lot of weight.

I use the same rod for tubes as I do jigs.

OK.  I want to throw 2 3/4" tubes with 1/4 oz weights.  Thinking of medium 6'8" to 7' casting rod.  Do I want it in F or XF?

Either will work fine.  You'll get more power in your hookset with the XF for the same effort, and may require drag loosening during the fight to reduce risk of tearing the hook out.  At this point it's a preference thing determined by you.  Everyone can just tell you what they like and why they like it but you may have different preferences.

The rod I am considering is the BCR802 GLX.  It will be my first GLX and I want to make sure if I am going to do it isn't a mistake.

If that's a Loomis, I would create a different thread on it in specific.  Many people here use them but they have different preferences.  i.e. Roadwarrior likes heavier tackle, others prefer lighter.  If you pick what someone else likes, but it's different than what you like, you'll have made the mistake you fear.

I personally would go with the BCR803 versus the BCR802 for jig application. I like the extra power when working jigs. I almost bought a BCR803 for jig use, but came to my senses after I saw the price tag :-[ I went with the Falcon Cara T7 6'10" MHF instead, and I love it. Like others have said it is now my "plastics and jigs" rod. As far as tubes go, I normally use spinning tackle with tubes because I mostly fish tubes weightless. I am no expert and have a lot of trouble getting a weightless 3" tube to go more than 10' with a baitcaster!