(This blog is purely opinion. I am not trying to endorse one over the other or anything like that.)
Achievements and Trophies are fairly new, created for this generation of consoles. They are both rewards for completing a preset "challenge" such as "Completed Chapter 5" or "Defeated 50 Enemies". Most of us probably know the difference between the two but for those that don't, I will summarize the difference in my own words.
Achievement: Xbox 360. An achievement is a reward in the form of points, known as "Gamerscore". Each achievement is worth a certain amount (Most games ranging from the lowest of 5g to 10g to the highest, usually from 100g to 150g). Most games contain 48 to 50 achievements with a complete total of 1,000g. A person's gamerscore accumulates over the course of completing more achievements.
Trophy: Playstation 3. Like the achievement, a trophy is a reward, but as the name suggests in the form of a trophy. Trophies come in four different kinds: Bronze, Silver, Gold, and Platinum. The difficulty of the trophies increases respectively (Bronze being fairly easy to obtain while Platinum is awarded for obtaining all other "Main Game" trophies. Trophies accumulate in the way of levels. Like difficulties, the percentage you receive from obtaining a trophy is worth more for a platinum trophy rather than a bronze.
So then which is better?
In my opinion, neither one is better. However, there are times where I would rather a trophy than an achievement and vice versa.
Situation 1 (Would rather an achievement): (Numbers are being exaggerated) An achievement is worth 100g but is a Bronze trophy.
Situation 2 (Would rather a trophy): (Numbers are being exaggerated) A trophy is gold but the achievement is worth 10g.
Although the numbers are exaggerated, there are real game examples similar to these situations. For example, the Bioshock trophy/achievement "Maxed All Tracks" is 50g as an achievement compared to a Bronze trophy. This is a perfect example of where the achievement would be worth more than the trophy.
Now to contradict myself from the paragraph above about "neither one is better", there are two times I would rather trophies over achievements. This time comes when a game is completed, meaning all trophies or achievements. Once a game on Playstation 3 is completed, you receive a platinum trophy. This brings up point #1. You receive something for getting all of the trophies whereas Xbox 360 simply shows that you gained a 100% in that game. The platinum also gives you a large percentage toward your next level. Point #2 is that the platinum is received when you complete the main game's trophies. An Xbox 360 "Complete" only comes when every achievement (including DLC) is obtained rather than just the main game's achievements.
What have achievements/trophies done to our game playing?
Trophies and achievements have changed the way I play games today, probably not in a good way. When I choose a new game to play, I sometimes base it around how many achievements or trophies I can get at the time. I don't replay older games because I feel that I should be playing newer games instead. However, I won't hesitate to replay newer games for a couple of trophies/achievements that I might need to go through the entire game again. In fact, I played through Dead Space three times in order to obtain all the achievements. I now at replay games at least once more (First time for story and second for achievements/trophies).
What makes trophies/achievements so appealing?
So why do I spend so much time working to get these things? Part of obtaining these trophies/achievements is to feel a sense of accomplishment. For spending so much time trying to obtain a trophy/achievement, it always feels good when it pops on the screen. Part of the obtaining is for bragging rights (Gaining a trophy, gamerscore, and trophy level). My friend and fellow Gamespot member GuitarAmp58 are constantly working together or against each other to obtain trophies/achievements. If one of us obtains a specific one, the other is determined to work at the game to achieve it too. As mentioned, we also work together a lot to gain a trophy/achievement or help one another gain one they already have. Whatever the reason, there is some motivation behind wanting to achieve a trophy or achievement.
Currently at 7 platinums and 7 Xbox 360 games completed, I'm always looking for the next game to obtain more trophies/achievements.
P.S.: The Xbox 360 sounds always mess me up. Friends logging in/gaining achievements should not have the same sound. *Shakes fist*