While they are under the same corporate conglomerate now they still maintain their individuality. While the T5Xi was assembled at the Burris plant in Greeley, they maintain their separate assemblies and did not cross over other than reticle. While most of Steiner's line is made in Germany, Burris seems to be moving more towards the US with their higher end (XTR III) scopes and are fully assembling here in the states; however, their other lines are still being manufactured in Philippines and other areas I believe.
Like ILya and Birddog mentioned above, you will not find shared parts, Burris manufacturers their own tubes and Steiner manufacture's their own tubes, they each have their own turrets and so forth, maybe some internals and small parts are shared, maybe glass is sourced the same but with different coatings but that's about where the similarities end.
As to your comment about the T5Xi being the scope you would pick today I would recommend you look at one before making that decision, the T5Xi had some of the worst CA I've ever seen in a scope and if you are used to Schmidt and Bender I think it would be bothersome, that being said I really liked the turrets on the T5Xi and wish other manufacturers would adopt the second rev window. While the Burris XTR III 5.5-30x56 seems to be a detriment at the bottom end, look at the FOV numbers and you'll find the 5.5-30 actually has wider FOV than most 5-25's do at 5x and FOV almost always trumps magnification in my book, so don't let the 5.5x vs 5x dissuade you (based on early reports it sounds like the XTR III is the better scope vs. the T5Xi). While the XTR II was definitely more the mainstream "budget" scope as you mention, the XTR III seems to be Burris' attempt to move up into the next tier, but instead of charging $2k street for the scopes, they are under $2k which is a plus as well especially if they can hang with the $2k crowd (I'm thinking Leupold Mark 5, Steiner T5Xi and even the Vortex Gen II and AMG series et al).
I have a 3.3-18x50 on order and hope to get it in hand soon to see it for myself as I'm very fond of ultra short style scopes that perform as well as their longer counterparts.
