UMK3 is like an upgrade of MK3 with more levels and characters. There were a few more extras in it. The best way to play it would be on arcade, which you would probably have to download the arcade emulator MAME. You would probably also need a controller that was somewhat similar to the ps2 controller. Thats the best way to play it.

Here's what got added between MK3 and UMK3, off the top of my head:

-New characters:
Scorpion, Reptile, Kitana, Jade (immediately selectable)
Human Smoke (pick robot smoke and hold back+HP+HK+BL+RN)
Ermac, ninja Sub Zero, Mileena (Ultimate Kombat Kodes)

-New stages: Desert, Khan's throne, Hell pit, Waterfront

-New moves and autocombos for some of the older characters: Stryker's gun, Kano's diagonal roll, Liu Kang and Sonya's launcher combos, etc.

-AIR STARTERS for autocombos: this probably changed the gameplay more than anything else. Now from a jumping punch or a straight up jumpkick, you can go right into an autocombo (this also makes Kung Lao's teleport much more useful).

-altered properties for some special moves and combos: Sub Zero's ice clone just disappears if you initiate it too close to the opponent, Nightwolf's aarow is now super-fast when used against an airborne opponent, damage for Kabal's launcher autocombo was reduced, etc.

-2 on 2 and 8-man tournament modes added

-Shao Khan's treasures added when you beat the game or win an 8-man tournament

-a few extra kombat kodes added

-For the one player game they added the super master tower and endurance rounds

That's all i can think of at the moment

Also they changed around the AI for the computer so that it will sit and wait for you now, allowing you to do the dance to eat the clock.

Roundhouses push you out of the corner (thank god).

Some other little things like Cyrax's air throw counts as part of a combo and a bunch of other little balancing things. But sadly, Kung Lao's spin infinites still survived.

Kung Lao's corner infinite was actually created by the new hitbox and properties it has in UMK3, in MK3 it was almost impossible to hit someone with a spin unless they were attacking, and oh yeah, the spin pushes you out of the corner in MK3, when they changed that is beyond comprehesion. It also didn't activate damage protection in MK3.

Here is a list of stuff I posted on TMK a while back when one of their resident morons said "ultimate mk3 has more characters, that is the only difference." sorry for the repeat stuff but I don't feel like filtering.

Aside from the obvious added charactes and stages,

Kabal combo damage reduced by about 10% total but the jump punch or kick starter is guaranteed off the spin, I guess the full damage would have been too much even though it doesn't effect his tier level at all.
Kabal's spin can only be done once per combo, so you can't spin in air, and then spin them again as they fall. This made setting up awesome corner combo in MK3 easy.
Jax single missile has huge recharge time.
Stryker has a riot gun (added move)
Shang Tsung's fireballs now require two hits between them to repeat. Example: aaHP fireball, aaHP fireball, in corner was possible in MK3, it is not in UMK3.
Smoke and Sektor's teleport uppercut comes up behind the opponent always, in MK3 it often came up infront of the opponent.
Sonya and Liu Kang have pop up combos (Making Sonya even more dangerous)
Sonya's leg grab now counts as part of a combo, and does 5%-2.5% after 3 hits or more juggled instead of full damage (In MK3 HP HP JK, Leg grab 4 hits 50%, 33% in UMK3)
Sub-zero's ice clone, does not freeze an opponent if you are too close to them, and this was an ENORMOUSLY ridiculous abusable tactic in MK3 that completely drops the character's tier level down.
Kung Lao's spin collision box is entirely weak in MK3 and doesn't turn on damage protection.
Kano also has a vertical cannon ball in UMK3, which is very helpful and makes him more Blanka like.
Cyrax's air throw doesn't count as part of a combo and his regular throw doesn't turn on damage protection, count as part of a combo, and does far more damage in MK3. (MK3 throw, LP juggle, air throw 3 hits 43%, 3 hits 17% in UMK3 but says 33%)
Nightwolf has a faster starting arrow if you do it while your opponent is in frames they do have control over even if they can block, or in other words any type of stun, blocking or not, for any duration, as long as the arrow is started before the last frame stops. The arrow only starts faster, it does not move across the screen faster, unlike Sindel's fireball after a grounded jump kick which I believe actually travels faster but I don't remember. The reason I explain it in detail is because this comment from TMK:

"Actually, Nightwolfs arrow comes out fast, when they are on the other side of the screen. if they are not on the opposite edge of the screen, it doesnt do it. heh "

Caused a 5 page thread of debating how Nightwolf's fast arrow works, since he is not "Total"ly With It..

The corner roundhouse thing makes combos like 5 roundhouses in one from Kabal possible which is INsane. aa RH spin, RH, RH, RH, RH, LK = 100%

There might be other stuff, but that is about all of it.

Today I was 8 on the Break and played this one dude for quite a while, he said at one point, "MK3 never should have come out, it should have just been this."

I liked MK3's stages better than UMK3's. The characters in MK3 also actually had pictures with their endings. But of course it didn't have the cool characters like Kitana and Jade, so that's why I play MKT to get the best of both worlds.

Oh yeah, add to that list, Robot Smoke's Harpoon has harshly different (better properties) it's faster and does not start behind him, also makes you bleed and makes a cool retraction noise, for those of you who interesting in asthetics.

Matt

Yeah that always seemed weird how the spear had no blood in MK3. I mean, it's a frigging SPEAR.

Also they added blood to Sub Zero's ice breaker fatality (the BL,BL,RN,BL,RN one)... or that might have just been in one of the pre-UMK3 updrades, i forget. I just remember it not having blood originally. And I think they added flowers to someone's friendship (Sonya maybe).

Sonya's friendship was the arm wiggle in MK3 and they made it flowers in UMK3, I don't think they come up on the roof top tage, she just stands there or something. They made little changes here and there on asthetics, but I'm more concerned about gameplay stuff as you well know.

Matt

UMK3 kicks any mortal kombat ́s ass and thats it