Browsing means searching for something specific while surfing means randomly searching for something.
Surfing is time consuming than browser because in surfing you have to read out lot of pages to get the desired result.
Satisfaction and information in surfing is more than browsing because when you search out for lot of material it results in increase of your knowledge.
Surfing is a wide term than browsing because in case of doubt on given resource, browsing converts into surfing to search for the reliable material.
I’d say that either “surfing” or “browsing” would be fine, and you should use whichever feels right for you.
My gut feeling is that “surfing” suggests the rapid motion of a surfer riding a wave, which wouldn’t actually allow much opportunity to stop and take in information. “Browsing”, however, suggests a more leisurely movement, with time to - at least briefly - look at what’s around you.
As the tools used to access the internet are referred to as “browsers”, I’d say that - despite the popularity of the term “surfing” - “browsing” is what you’re actually doing if you’re using a browser.