The two are totally separated. You spend your advancement points on common skills. You spend experience on combat skills and Valor/Wisdom levels. And they reinforce thusly what you've been doing with your time.
SPENDING EXPERIENCE POINTS
Heroes may spend their accumulated Experience points
to gain a new rank in either Wisdom or Valour, and to
enhance their proficiency in their Weapon skills.
(TOR AB p. 170)
Note that it does not list common skills there. Thus it's not allowed.
SPENDING ADVANCEMENT POINTS
Players spend Advancement points to raise their Common
skill ranks, using the costs in the table below.Players
are not obliged to spend all their Advancement points,
but may save them to acquire more expensive upgrades
during a later Fellowship phase. Players can also buy
multiple ranks into the same Common skill, as long as
they pay the cost of every new level individually. Any
remaining Advancement points are kept track of using
the appropriate space on the back of the character sheet.
(TOR AB p. 171)
AP are pooled - at the fellowship phase, all your marks are tallied, and then you add that total to your available AP. Note that there are only 3 AP per category, and unspent go in the single box on the back of the sheet... and the lowest cost upgrade is 4, so it's impossible to use a single category's AP total to raise a common skill.
Yes, the system worked quite well for me - the separation of AP and EP forced players to use their common skills in order to raise them. Combat is easy - XP are earned pretty steadily. The gaining of abilities and magic item by Virtue and Wisdom ranks worked particularly well.