The Redwood is slightly more accurate than the Spider, but less forgiving on mishits. It also has a faster meter speed than the Spider. Successful putting is partly about having a good feel on the greens with the tempo of whatever putter you use, so if you like the feel of a slower meter with your other clubs, then go with the Spider. If you like the faster speed, then go with the Redwood. The variety of balls can slow the meter down even more, so it's largely about testing different combinations to find what suits your game.
Both putters are big upgrades from the basic putter, and will help in the long run.