Now that I've had a chance to read the 4E PHB and DMG, and DM a couple of 4e adventures, here is how I think d20 modern would be impacted by 4e, trying to be as objective and factual as possible (underlined phrases are are caveats). Not trying to lean one way or the other, just putting out a 'few' observations:
1) Characters could take more punishment: current starting HP is around 6-15 hp depending on class and con.
In 4e, starting HP are anywhere from 18 to 38. (The 18 is for a Wizard with an 8 Con, the 38 for a fighter with an 18 con).
2) Skills would be combined and streamlined: : In modern, sleight of hand and disable device are two separate skills.
In 4E, they are combined, along with pick pocketing and detecting traps, into one skill called 'thievery.'
3) Characters healing ability would be better: In modern, ability to restore HP is limited to one treat injury per day, surgery, and recovering a few hp a night with rest. Massive damage can drop someone to -1.
In 4E, you get 6-10 healing surges a day, which allow you to recover 25% of your HP at a time. You can do it once per encounter (combat) as well. And, if I'm reading the rule correctly, a night's rest (extended 6 hours) gets you back to full HP. There are no massive damage rules.
4) Multiclassing would be limited: In modern, switch character classes as many times as the GM will grudingly let you do it, picking up unique class talents along the way.
In 4E, you remain, one class, but you can pick up abilities and powers from other classes via race or feats, albeit at a lower level than your main class. You are also limited to dabbling in one other class.
5) No more multiple attacks w/o a special ability: Modern allows multiple attacks based on your BAB, weapon, and fighting with two weapons.
4E doesn't allow for two weapon attacks or double weapons unless you have a specific power that allows you do to so. Instead, attacking with two weapons lets you do +1 damage with your main weapon. So far I haven't found any rules that allow for multiple attacks based on BAB.
6) Action points are slightly different: In modern, action points either let you activate a talent or add to a (usually bad) die roll. You get around five per level.
In 4E, Action points are sometimes also used to activate powers, and are also used to allow a player to take an extra action (such as two standard actions) during his or her turn. You get one point per day and may get more if you get in a lot of fights.
7) Actions are different: In modern, you typcially get standard, move and free actions during your turn. You can also ready actions.
In 4E, you get Standard, Move, MINOR and free actions. You can also ready actions. MINOR actions are for drawing a sword, maintaining an ongoing spell, drinking a potion, etc.
8) Powers:: 4E has special class and race-based powers that allow characters to take special actions in combat. The powers are essentially divided into:
'At will', which can be used once per round. Example: Wizard casting a magic missle or a fighter trading damage for a more accurate to hit roll;
'Encounter', that can be used once per combat. Example: a cleric turning undead or a fighter taking swings at two adjacent opponents with one standard action;
'Daily', that can be used once per day. Example: a fighter being able to do triple damage if he hits, a wizard casting a sleep spell.
These powers remind me a lot of the special attacks video game figures use when you press the right combination of keys (down twice while pressing the A button and Kung Fu Master exectutes a spinning pinky punch.
9) Saving throws are different: In modern, you have will, reflex and fortitute saving throws to avoid certain adverse effects. If a bomb goes off, you make a reflex save to avoid damage.
In 4E, you have defenses that must be overcome with an attack roll by the spell caster. Thus the bomb would make an attack roll vs. the target's reflex defense score
The only time you roll saving throws is to avoid a continuing (ongoing) effect, and then you don't add modifiers, it's a 55/45 chance in favor of the player.
10) You can become bloodied: In modern, you can act just as easily at max hit points as you can at 1 HP.
In 4E, when either you or your opponent gets to 50% HP, you become BLOODIED. Your opponent may have powers that work better when you are bloodied, making you more vulnerable. You may have powers that work better, making you more powerful. Also, certain conditions in the adventure may not be triggered until someone is bloodied.
11) Non-lethal is different: In modern, you can grapple, trip and throw non-lethal punches to knock someone out.
In 4E, there is no such thing as non-lethal damage. If you want to knock an opponent unconcious, simply declare that as they drop to zero HP.
Instead of grapple, there is grab, which simply allows you to hold an opponenent in the square they are in. The PHB doesn't have any rules for pinning that I saw.
12) I could go on and on and on: dying is different. Weapon proficiency is different. Character advancement is different. Instead of detailing them all, I'll end with a few observations:
4E HP rules would make characters more powerful and harder to kill.
4E healing rules would make it easier for characters to continue on their mission rather than return to base and rest. Those same rules would take the lethality of of gun combat.
4E class rules severely limit the ability to customize characters and create unique multi-classing options.
4E class encounter, daily and at will powers lends themselves to a superhero an action movie type game where characters can get shot many times but still pull off that Jet-Li Like 'Dancing Democratic Donkey Sytle' kung fu kick.