Aldrige is the better player right now, Thompson needs to prove more consistency and solve his foul problem. None of them is a good post defender, physical big men have their way with JT, but with JT (and the hustle of other forwards), the Kings' lane is no longer layup drill, LMA has the better mid range shot, but JT's awkward hook shots in the post are effective and his jumpshot is very good for a big man, Thompson's rebounding edge is affected by the lack of dominant rebounder at the C on the Kings, I'll call them equal there.
In terms of talent, potential and even physique they are very similar players, JT's erratic play and fouling issues set him behind a little bit.
As far as defense, I'd say Aldridge is better. The numbers tend to support that as well. Now, Thompson plays a lot of C while Aldridge does not, so sometimes the comparisons are skewed a bit by something like that.
Aldridge has a significantly better defensive rating then Thompson, 104 vs 111. Aldridge also has better a defensive win share number.
And as PF's, opponent numbers reflect better defense on the part of Aldridge:
opponent eFG: Aldridge .486....Thompson .560
opponent FT attempts per48: Aldridge 4.8....Thompson 5.5
opponent rebounds per48: Aldridge 10.1....Thompson 13.4
opponent points per48: Aldridge 19.8....Thompson 23.1
opponent PER: Aldridge 15.9....Thompson 21.9
Aldrige plays with 2 great defensive Cs, Portland's defense is much better because of that and it goes across the board for all players.