Probably depends on your gear as well, but bass strings absolutely make a difference as far as I'm concerned. The type of string is a basis for shaping your sound.
There was a great article in Bass Player years ago that went through and listed attributes of just about every major bass string on the market. Took a while to track down, but the following is a link to their assessment. As a 26yo bass player, I haven't had a ton of money to go try different amp/head/bass/string combinations, so this was a great shortcut for me. I still have the hard copy in the studio for reference.
I hope this helps!
I'm currently using a brand name string that has a tendency to whistle a lot and I don't personally care for that sound nor the feel of my fingers getting a ground up by the edges of it. I know I sound like a cake fed nurd.. but I am spoiled to coated strings.. I have them on nearly every bass I have and they DO last much longer..
I do tend to use Carvin strings on my Carvin basses. It's primarily for tension reasons-D'Addarios tend to pull too much. I do find that different basses will speak better with different strings, so I will use Labellas on my Modulus basses, D'Addarios on my Fenders, Carvins on my Carvin and Dean Markley Snakeskins on my Conklin.
I find that I can't use Stainless Steel-too bright! I tend to use Nickel round wounds and my absolute secret weapon is the 20 year old Ground Rounds on my 1973 Fender Mustang Bass. Can you say "Americana approved"?
As Bryan Beller so wisely put it, the signal chain starts with your hands, then your strings, bass, pickups, cable, amp or preamp, etc. They're all different factors.
I guess all in all, I'm pretty finicky about strings....
I used Ernie Ball Bass Slinkys for the longest time, but I like my strings a little broken in - with those it would take several months before the brightness wore off and I could control the tone better.
I recently switched to Rotosounds, and they are wonderful; they have that "broken-in" sound right out of the box, and feel great to play. My only concern is that the B string feels a little messy to me, but I'm going to stick with them a bit longer and see how they record.
Strings are a critical part of the tone equation. Like Roy stated I have different strings on different basses for different types of music. I also believe that roundwound sounds better in a live band mix and flats sound better recording but thats for me, and I dont normally slap.