Newegg is better for customer service by far. I've only had one problem with Tigerdirect customer service but it was a big one. A box was never marked as leaving their warehouse, assumed lost. I was promised an overnight replacement, but it was shipped standard and missed a deadline. When I went to return them the best they would offer me is a $20 credit which didn't even cover the return shipping, and I had to fight with them to even get that.
Newegg on the other hand seems to go quite a bit further to help their customer. They allow advance RMAs on request and will even cover return shipping. On one occasion something arrived damaged and it was clearly their fault (hard drive improperly packaged), they overnighted a replacement and offered me a $25 credit even though I was happy with just the quick replacement.
On the other hand, Tigerdirect occasionally has unbeatable deals on certain items. I find they can be good for low end things like flash drives and cheap routers. They also will have great deals on barebone kits and laptops. Then there is the added bonus that they have a warehouse a little over a hundred miles away. Sometimes I'll orders something late afternoon one day and get it the next morning.