What makes one assault rifle 'better'. Well, to answer Nolo:
308 is out. Totally uncontrollable under full automatic fire. The assault rifle is a multi-role weapon. One of the weapons it replaces is the SMG. There are times when automatic fire is appropriate - particularly in the assault, or when engaging moving targets where only a brief exposure of the target occurs. Or when suppressing a target during fire and maneuver. The amount of time where aimed fire is actually possible and appropriate is actually rather limited in modern mobile warfare.
Rounds should be relatively effective at normal combat ranges. Despite conventional wisdom, the 5.56 was 11% more combat effective (lethal) than 7.62x51 in Vietnam. This is mostly due to the performance of ball ammunition. See
http://www.fen-net.de/norbert.arnoldi/army/wound.html
223 rounds are lighter than 308, meaning that more ammunition can be carried.
As for the weapons remaining, two stand out - the AK-74 and the M16. The AK is a derivative to one of the best military small arms ever made. It is utterly reliable and has increased lethality over the 7.62x39 version. It is combat proven.
The M16, while initially have teething problems, is now a very mature and reliable weapon system. It does require maintenance. It is far more accurate than the AK, and thanks to its modular design, lends itself to an amazine variability. Modern versions feature integrated picatinny rails in every location imaginable. Barrel changes are trivial.
The direct gas action, derided by many, makes for a very light weapon and enhances accuracy as there is no moving mass on the barrel like piston operated rifle.
The M16 and the AK have been in the field for over 4 decades. Having looked at some of the newcomers, I am not impressed. The L85 has a horrible reputation for reliability - even after HK made a number of improvements. The AUG is not well like by the troops I talked to (Kiwis) to whom they were issued.
The M14 and FAL are really only suited for DMR these days, and in that role, the M14 wins the day. The FAL has a horrible trigger that is basically unfixable, and does not lend itself to accurizing or optical mounts like the M14 does. Both are inferior to AR-10 derived SASS. Go to any service rifle match and the AR derived rifles rule that event.
G11. Interesting concept, but a 19 caliber bullet!? This is loved by people who think the P90 is actually useful against people who are shooting back at you.
Galil - superior weapon but heavy. I would not feel undergunned with a Galil.
FNC - a rifle that deserved better than it got. a Simplified AK gas system using Johnson style locking. The SCAR might be an improvement, but it is too early to tell. The FNC lacked flexibility. No easy way to mount different optics, lasers, etc.
HK G3 - FAL with a worse trigger and the ergonomics of a 2x4. Delayed blowback in a 308 is scary. HK itself abandoned roller locking in all of its rifles. Ejected brass is almost as dangerous as the bullets.
G36 - an AR-18 in different clothes. Some improvments, but it felt flimsy and was very uncomforatble after extended full auto fire. The XM8, a tarted up G36, did not do well in tests. This is a great rifle for people who don't plan on being in combat much. It way to expensive for what you get. Favored by the trendy.
The FN2000 looks promising from the perspective that they have solved the right/left eject issue with bullpups. It suffers from the same issues as other bullpups - magazine access is awkward. Bullpups get there butts kicked in tactical matches because the aren't as user friendly when it comes to stuff like reloading.
Finally, to address the shotgun - it is a very specialized tool. Even with 00 buck, effective range is really only about 30 yards. Sometimes, you want a little more reach - actually, most of the time.
There are a few new designs that seem to have promise. I am particularly intered in the MagPul Masad, mostly because their rifle is evolutionary, and because they have been turning out first class products for a while. But I won't be impressed until it's been around for a while, and some grunts get their hands on it.
The above are only my opinions, based on my experience with a number of class III and civilian versions of the above. YMMV