By drilling out the main (long) tube, you've destroyed its tensile and bending properties. You don't come even close to getting them back by transferring longitudinal stress in the long member to transverse stress in the walls of the Tee-leg.
Another poster talked about controlling weld distortion. If you leave the long tube intact, its structural integrity means that weld distortion will be much more difficult to control/correct (especially in stainless.) On the other hand, the predrilled joint will be much less sensitive to distortion and easier to straighten out what does occur _because_ of its inherent weakness in that direction.
Don't take my word for it. Take a couple of pieces of tubing each a couple of feet long. Weld a drilled tee joint in the center of one, a fishmouth joint in the other. Line them up afterwards to compare distortion. Set them up spanning a pair of tables. Load them with something at the weld joint. Measure natural frequency. Measure deflection as a function of load. Load them to failure. Report back here.
It really boils down to your structural requirements on the long piece. If it's a primary load-bearing member, don't prep it and deal with the distortion some other way. If it's cosmetic, then it doesn't matter.
After you make a couple hundred fishmouth joints, you get the idea why people like square tubes. They're far easier to jig, weld beads are far easier to run, and it's easy to design machined preps to meet special load conditions without destroying basic section properties.
Hth. Fred Klingener