This is all my opinion.
I think both systems appeal to different types of people and every player should know the pros and cons of both.
A skill based system offers immediate rewards as a player is able to accomplish more in short sessions. The rewards may not make your character more powerful, but it's the thrill of successfully making it through challenging content that is the bulk of the fun.
However it requires a player to put themself into the proper frame of mind to figure out how to use their skills more effectively in order to accomplish such difficult tasks. If you aren't in that frame of mind, or not the type of player who cares about playing that way, challenges in the game can be quite frustrating and gameplay not as much fun.
Certain tactics will be found that can more easily get through content, lessening the rewarding feeling of accomplishment. Also the lack luster physical rewards given after each accomplishment often don't offer much incentive to invest much time with a particular character. Your characters don't noticeably become more powerful the more you play. Character's power potential is instead tied to the player simply becoming better at playing the game.
A time->power based system's enjoyment mostly comes from anticipation and physical reward. The gameplay is usually much easier and can often be considered trivial. It's intended to be doable with out too much emphasis in being as effective as possible in skill use.
However it's the anticipation of being rewarded in physical ways that make your character stronger which fuel the enjoyment of playing. It's much easier to feel rewarded in this system, if you have the time to invest, as the rewards are quite noticeable as your character grows more in power and can more easily breeze through content found earlier in the game.
Unfortunately it requires quite a bit of time to get things done. Short sessions usually see little gain. Also as characters grow stronger in power, content can become more trivial and the enjoyment becomes more and more dependent on more powerful rewards, which leads to what is called 'power creep'. There becomes more and more of a disparity in content as it scales to characters' power levels.
Starting a new character is far less fun as you are forced to replay all the old content in order to become powerful enough to see newer content. Longtime players eventually start complaining that there is not enough endgame content for their oldest, most powerful characters.
I've seen this happen alot in WoW and EQ2.
Honestly, I hate both systems.
But I hate the skill-based system less and I feel using the skill-based system as a base a new system could be developed that ensures that players will not only enjoy the thrill of getting through difficult tasks without the need to meticulously study skills' effects, but also offer incentive to continue playing with one character by offering fun rewards, that don't necessarily offer more power to a player, but instead offer more creative and interesting options.