There's a difference in the amount of experience gained for each difficulty level.
There's no exact number but here and here it's roughly 250k experience to level 15.
If killing a monster at normal gives 100 xp, killing it at Expert would gives 200 xp. You'll level up slightly quicker but since the amount isn't that high, the difference is less noticeable.
Also, from experience of getting 5 characters to level ~10 in hardcore (in case of...), I noticed I could be level 10 with one character when finishing the quest to get Cain out of trouble while I also could get it well before with others. I did that at the same difficulty (hard).
The difference came on how much time I took to find the right path in the cemetery, so how much monsters I killed. So even at normal, if you kill more monsters, you'll gain roughly the same experience as on expert if you kill less. I also did the quest with the lady ghost after one or two characters as it can give good items for your level, which made those characters get 10 before getting Cain out. Doing it at normal and not expert can also lead to a smaller gap.
All that to say that the more you'll kill monsters in expert mode, the more experience compared to normal will be gained. If you take the time to clear every monsters, do every side quests, in both difficulties (normal and expert), you should notice a difference, even so small as it might be (like a level or 2 more in expert).