The results are basically the same if the volume pedal is passive - isn't it just a pot on a treadle anyway? Your guitarist doesn't know what he's talking about, and I don't know what he's talking about either...
The one advantage a volume pedal can give you, however, is foot control of your volume (instead of using your hands). But unless you're doing violin-style volume swells or changing your volume frequently, you probably don't need a volume pedal. Most bassists I've known never use one.
Now, if it's an active volume pedal (a la Morley, Visual Sound, etc.), then it's a bit different. You can get a gain boost from those kinds of pedals, above and beyond what your bass puts out when the volume knob is maxxed. It does introduce a buffer and a new circuit into the mix, though, so you might get a very slight tonal change (good or bad? You decide). But if you just need an instant boost in gain, consider a simple boost pedal instead - it'll take up less board space and require only a stomp instead of a sweep of the foot.
So, unless you need variable control of your volume that can be managed by your foot, you don't need a volume pedal IMO.