Either way will work fine as long as the tenons are a good fit on the wider side. The strength in a glued tenon joint is in the wide flat surface area: the more that fits well, the stronger the joining. Theoretically, that means running them together gives a stronger joint. However, each tenon must be trimmed shorter than the depth of the intersection to prevent interfering with each other, pretty much negating any extra surface area.
Running the mortises together can cause a couple problems that can easily be avoided, but you should be aware of:
1. Tenons too long causing interference with each other. (When doing this, I miter mine so that there is at least a good 1/8 between the ends and double check the shoulder fit with both pieces clamped into place)
2. Glue/chips pushed into the first joint can run into the intersecting mortise, causing problems when gluing the second one. Not a big problem if the mortise is well cleaned and both sides are glued at the same time. If not gluing both sides at the same time, the dried glue can really mess up your day trying to clean it out to fit the second one. This can be a major headache if using expanding glues like the urethane Gorilla Glue, etc.
If you are going to glue up the sides first, and then put in the end aprons (or vice versa), you may have less problems going with a mortise depth just shy of intersecting. If hand chiseling the mortises like I do, that can often be close to impossible, so I make sure to thoroughly clean out any chips/splinters from the bottom of the mortises and I have enough clamps and a large enough work area to glue all at once.
Hope this helps.
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