There is a noticeable difference, yes. The biggest differences I've noticed rely on what the analog outputs have for op-amps and what the software allows for EQ tuning and shaping and the form of signal boosters. Going from onboard years ago to an old X-Fi Xtreme Music was a MAJOR difference. Going from that card to a much more expensive Auzentech X-Fi Forte was a slight difference but that card better handled the style of sound I liked (bass heavy), and had a headphone amp on rear and front outputs.
I also own an Aune T1, which is a solid investment if you want a quality and affordable external sound solution.
Something else to keep in mind is how you drive what you're listening to. Right now and for over a year I have been using optical to my Denon AVR 1613, relying on my sound card only for its EQ. I recently removed the sound card due to driver issues/bugs I was done dealing with and downloaded Equalizer APO and then found a 32-band EQ to tune my wound with.. My onboard is the not-stellar Realtek ALC1150, and it is doing a fine job of sending the digital sound signals to my receiver. What am I getting at here? Well depending on your output choice you may or may not notice. If using digital, odds are you won't notice from your sound card... my Denon is doing processing to convert the sound to analog at this point. I am again pushing an EQ'd sound signal to my receiver.
Now if you are using your analog connections, then a better sound card will make a difference. Going from the onboard ALC 8xx series on my old lady's P61 board (specs in sig), to an Asus DX or GX ($30 PCI version) was very noticable. We have an old pair of refurbished Logitech X-230's and they also use headphones on that PC a lot...so direct analog connections to the PC. This is where a good sound card can make the most difference. A good sound card does not have to be $100, 200 or 300+. Really, I feel that if you're used to cheap sound...and you feel it sounds good, you might not find the value in something that creates a similar sound that costs way more...depends on how sensitive to sound changes you really are.
I really like the cheap Asus sound cards, even with stock drivers. I also miss my old X-Fi XtremeMusic, that card was truly a gem. The Auzen Forte is good, but its drivers were a nightmare and newer drivers are no longer being made for this card that I could find...there were some from one or two years ago iirc.
It really depends on the sound you want too...honestly it pays to keep it simple because audio gear gets expensive very fast. I got into audio, next thing I know I have a $300 pair of Denon D2000's, a $120 sound card, a $250 receiver, a $400 pair of HE-400's, a $100 pair of JVC HA-DX3's, etc. etc. etc.... and honestly I've stayed on the cheaper side of things. Other users here can add a couple zeroes to the end of what I've spent.
If you're happy with it, don't change it, if you want change, be specific in what you want from your sound and if possible go somewhere and test different hardware (tough to do for many).