Who will win?? I will try to pass on a non-biased judgment here, using my expertise as an Infantry Officer.....
First Question you need to ask, will Nuclear Bomb in plays? (I don't think NK have the skill the mininaturize the fission material for warhead) So, will Nuclear bomb in plays.
Second Question, who shoot first?
Pre-battle Assumption
You can discount both Navy (assume US do not response in Naval Blockade) both Navy do not have enough to lay a blockade on each other territorial water. So, as most both navy are used as Naval Bombardment for hard target on land.
Air Force, NK airforce currently have in ivnentory
40 Mig-29
50 Mig 23
200 Mig 21/F7B
100 Mig 19/F6
100 Mig 17/F5
South Korean Air Force have the following
60 F-15K
210 F-16 (All model)
70 F-4
170 F-5E
Assume the kill ratio
F-15K : 1.5 Mig 29UB, 2 Mig 23, 3 Mig 21/19/17
F-16 : 1 Mig 29UB, 1.5 Mig 23, 2 Mig 21/19/17
F-4 : 0.5 Mig 29, 1 Mig 23,21/19/17
F-5 : 0.5 Mig 29/23, 1 Mig 21/19/17
After the initial engagement, ROKAF will have the air dominance of
30 F-15K
85 F-16
0 F-4
0 F-5
South Korea achieve overall and regional air dominance.
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Now, if war started by the North Korean Side. North Korean can probably penetrate 10-20 mile inland (Over Seoul, the capital)
before being driven back by combine effort of air and land force of South Korea. First day of the war would see the destroy of the air power of North Korea, and tactical communication hubs, transport hubs of North Korean near the Border of the south. Without them, NK will suffer a resupply problem and while ROKAF roam the sky and ramdomly attack supply column driven to the south. With a further defensive line in Inchon-Gyeonggi-Gangwon defense line, mark the begining of hill area. Unless NK have way to evade ROKAF CAP. this would be where the offenive line of NK drew. Would take appoximate 1 weeks to 20 days.
After the first 20 days. Where the attacking NK force used up 50-70% of supply, unless they are to fight hand to hand, they will need to withdraw. The ROK Army will push from 2 entry, covered by air support and artillery strike. 30 F-15K could have destroy 50up to 70 armored target per sortie with the effective engagement rate of 90%. plus another 85 plus F-16 can achieve a 40-50%destroy rate of North Korean armor.
That will leave NK down from 5000 MBT to effective 2400-3000 MBT. and face off with ROK Army's 2500 MBT. Assume the kill rate is 1 : 1 in the end, the South would have come out ahead in any plateau fight as ROKAF gain air superiority localling and nationwide.
By now, the North assult should be all but die down, there are two option for NK ground force. Either retreat back to NK or hold out and call for more troop, bring up the reserve. By this time, estimated troop loss will be about 20-25% for North Korea (based on the ratio attacker/defender 2:1 without aircover only artillery cover.) and ROK ground force will be about 10%. While in the air, ROKAF continue pounding the NK massing point and rally point, thus create more casualty for NK gorund force.
It should be note that without air cover, ground troop assembly rate are about 70-80% effective (assume 4 rally point with 4 entry route corresponding to NK Army station before the war. With ROKAF have 20% interdiction rate. There are literally no way NK can punch tho the 38 parallel again. Because either they need to move their AA defence ahead of the marching column, and set up and wait for infantry and armor to defend them, thus casue casualty on the AA, or they need to leave the AA defence behind and move their infantry and armored without any AA cover, thus cause casualty on them. In this case, losing a chuk of raplceable infantry would be much perferred than losing a chunk of non-replacaeble AA defenses.
So this indicated to a battle of attrition. See who lose more first, did NK lose enough troop or ROKAF lose enough aircraft first. In all, there are no futher chance for NK to move across the 38 again without putting out their AA defense as cannon fodder.
Will the South Counter attack is another issue