There's a few neat tactical elements that come out of old school initiative that are worth considering:
Intraparty Action Order
Notice how Missles>Spells>Melee within any given side? The important thing to note about this is that ranged weapons will never get the benefit from spells in the same round, while melee can always gain the benefit of spells in the same round.
There's also considerations as to which order people move/attack for the sake of placement or not wasting actions.
Declarations and Nullified Actions
If the enemy wins initiative and ducks behind cover before you can shoot an arrow, you just wasted your action. If you win initiative and get into melee with the enemy, they don't get to run without risking another attack, etc. (This becomes really nasty when you combine it with morale rules - you hit first, they run, you hit again...)
A/B/A style of Old School Initiative
I swear I've seen this elsewhere as well, but Philtomy's D&D ideas about initiative take the same basic structure but instead of one group goes (move/missle/magic/melee) it lets them go back and forth within that.
Philtomy's version is a bit more in depth, but a simpler version to consider is:
Group A fires Missles
Group B fires Missles
Group A casts Spells
Group B casts Spells
Group A Moves (Either full or 1/2)
Group B Moves
Group A Moves (if they've moved 1/2 before)
Group A Melee
Group B Melee
This means the group has to really think about who they target and where they place themselves and what order.
Winning Initiative is a big advantage
In the old school method, you can see your side can get several attacks or spells in consecutively - which makes it more likely for you to knock out at least some of the opposition - when an opponent is down it's not returning the favor. Given how low the hitpoints were for many characters/creatures, you could quickly wipe out a fair number of them and get them to face a morale check.
Initiative modifiers are based on teamwork/larger conditions
Since you're rolling for a whole side, you don't have to track each monster's modifiers for initiative - it really only comes up if it's a group of the same type and they have some kind of special ability ("Surprises people 3 out of 6 times because they're NINJA werewolves" or whatever)..
This is either a feature or a drawback depending on how you want to look at it. Sure, the fast guy is probably going to go before everyone else, but in a large team fight when you have combat rounds that are a minute long, we're talking a different scale than a single attack or two.
New Individual Initiative
The individual initiative systems allow a lot for specific characters to have bonuses/modifiers on different things and getting to go first, "ready actions" and all kinds of tactics around that.
On the other hand, outside of readying actions, you pretty much are 100% crap shoot as to which order characters go in, which means coordinating spells or combined actions ("No, let me shoot him with the arrow before you run in") becomes significantly more complicated for players to deal with (many groups never figure it out and just give up on that kind of teamwork altogether).
It also takes longer to adjucate and you end up tracking a lot of initiative round to round.