An important factor is going to be the condition of the T1-11 (old, weathered, aged, warped, etc), and whether it is properly secured to the framing.
You can go over the T1-11 with sheetrock (we have done this many times), However, just make sure that the T1-11 is properly secured to the framing underneath (no loose, warperd, or flexing areas).
In such situations, we always (yes always - regardless of loose sheets or not), add additional screws or ring shank nails to the sheets of T1-11(fastened into the framing), to ensure that it is solidly attached to the framing. If you have weaker areas, the newly attached sheetrock will eventually crack at nearby seams.
Also, make sure that the urface areas of the T1-11 is flat, and not uneven, or humped. This can be done by holding a 6' level's straight edge to the surfaces. If it appears that the T1-11 is just not linear (flat), then you may opt to just take it all off, and attach your new sheetrock directly to the framing. (There are times that we have had to do that too).