How will the honor of Bayis Sheni be greater than that of Bayis Rishon?
Rashi citing Bava Basra 3a: The Binyan will be greater. Radak - there was never a building as good and beautiful as it 1 .
Bava Basra 3b: It will last longer. (Rashi - it lasted 420 years; Bayis Rishon lasted only 410.) Also the first answer, it will be taller, is true.
Malbim: It will not be destroyed. All this is conditional - if there will be another Ru'ach, and they will fulfill the Bris that He made with them when they left Egypt, then it will be the last Bayis, and it will be greater than the first. The condition was not fulfilled - they did not guard the Bris, and there was not Shalom there. There were many Peritzim, factions and Sin'as Chinam. This prophecy will not be fulfilled until the final Bayis is built at the final Ketz.
The Gemara learns from our verse that Bayis Sheni was taller! (PF)
Why does it say "Eten Shalom"
Radak: Even though there were many wars in the time of Bayis, there was Shalom in the land for a long time.
Malbim: There will not be Sin'as Chinam among you. This caused Churban Bayis Sheni!