Restricting ourselves to the events of UC 0079 to UC 0080, even a quick look at force deployments and in-battle performance indicates that Armored, Mechanized, and Naval formations will change utterly as Mobile Suits are more thoroughly integrated in the armed forces.
A quick look at the Battles of the Loum and Odessa shows the importance of Mobile Suit deployments. At Loum even an early deployment of original-run Zakus (Who didn't have so much as a beam gun between them) utterly changed the tide of battle, converting what would have been a rout into a decisive Zeon victory. At Odessa the sheer mass of Federation troops resulted in a Federation victory, but the literal millions of troops necessary to defeat relatively few Mobile Suits (Admittedly with tank and air support) shows the raw strength of the suits design. An army that does not deploy Mobile Suits is, very simple, obsolete. Barring one-off prototypes like Big Zam, the Mobile Suit is necessary for a modern army to fight off another modern army without an overwhelming numerical advantage.
While the snap response to the last part of your question is to say that Zeon best utilized the new technology, a more comprehensive look at combat during the One Year War would indicate that this is untrue. While Zeon fielded an enormous variety of suits their refusal to standardize until late in the war, rivalries between various commanders interrupting the deployment of new Mobile Suits to the front (See, Ramba Ral's death as a result of Kycilia Zabi's refusal to equip him with new Doms), and the variety of suits being deployed overtaxing Zeon's already exhausted manufacturing capabilities crippled Zeon's use of its Mobile Suits. At the time of the Battle of Jaburo Zeon was attempting to manufacture and deploy Zakus, Goufs, Doms, Z'Goks, Goggs, Acguys, specialized Mobile Armors, and specialized Mobile Suits, and was undergoing R+D on the Hygogg, Efreet, Gyan, Gelgoog, Gelgoog Jaeger, Kampfer, and Zeong all with a manufacturing and resource base significantly smaller than the Federation's.
Meanwhile the Federation used a relatively small variety of mobile suit models to great effect. The Gundam, Gundam Ground, and GM could generally swap equipment and were all more than adequate suits for all uses during the one year war. They each saw enormous success that capitalized on the Federation's strengths, allowed for relatively simple logistics (Gundam Ground-Types could even have parts replaced with GM parts in the case of material shortage on the ground) and, very simply, won the Federation the war.
Ultimately little, the Veritechs are a far superior platform and can be launched from existing Super Aircraftcarriers with no modification. Those nations that adopt the Mobile Suit platform will be doing so as a replacement for existing tanks and will most likely be used as parade units rather than deployable forces by first rate militaries.
The Mobile Suit is far too expensive for the capabilities it provides, and, although units are operationally deployed with them, there are still significant problems with their organic life support systems.