Nickel has a duller/warmer, yellow-ish undertone to the color. Chrome is more mirror-like and has a more blue-ish undertone. Without seeing the pieces, I can't really be sure. Can you post some pictures?
Generally speaking, chromium plating was the more-"deluxe" finish because it was harder and more corrosion-resistant -also more costly because it was an additional step in the metal-plating process. However, nickel that's in really nice shape has a richer look, in my opinion. It reminds me of what real silver looks like. However, it's more difficult to maintain and quite a bit softer than chrome.
I think some mild silver polish would probably work great. I've also heard that j eweler's clothes (?) are something that works well on nickel.
When I clean chrome pieces initially, I usually take them and soak/spray them with WD40 and then I get some terrycloth towels and paper towels and take the stuff out on my porch and polish them until they are as perfect as possible. I wipe them with dry towels and rags until they are clean and then, from that point, I try to maintain the look with a bit of Windex on a soft cloth.
Fingerprints are the worst offenders to nickel finish because the nickel is very reactive to even the slightest amount of skin-oils. That's why you should never touch nickel with bare hands if you want it to stay looking clean.