Westwater, class III(IV-), is significantly easier than the Lower New, class IV (IV+). Westwater only has one class IVish rapid, Skull. The lower New debateably has 5 IV's and one IV+, Double Z - actually if you ask the outfitters it is class V brah!
The Lower New often has more volume - annual high flows of 60,000 to 70,000+ cfs are fairly common, and unlike Westy it doesn't flush out completely - it gets huge holes, like when Whale Rock starts going under. Westy in Sept is likely around 3,000-4,000 cfs, which is actually quite comparable flow wise to the New that same time of year. The big difference is that Westy isn't nearly as rain driven and won't bump up to 40,000 in a couple of days if a big rain event hits. You can still flip and swim on Westy, but if you are comfortable on the Lower New then Westy should be well within your range. Remember to pack lot's of ice cold beer - early September can be hot.