Well, the Andaz is right in the western canal belt, by the 9 Straatjes and Jordaan, handy for the Westerkerk, Anne-Frank-Huis, not far from the Noordermarkt, etc, etc. Lovely area - laid back with plenty little cafés and restaurants to eat at.
The Renaissance is right in the tourist heart of the city, near the station. Turn right, and you're on the canal belt, turn left and you'll hit coffeeshops and red lights pretty quickly on Spuistraat. The area's slightly grungier, but there's no denying how convenient it is.
I used to stay at the Renaissance sometimes on trips there, and never particularly got on with it. I found it quite staid and dated, but pleasant and clean enough. It may have been refurbished since - I couldn't tell you.
Personally, I'd go for the Andaz. It's a small city.