A possible reason for the differences in minhag is based on a disagreement etween the Baal haMeor (Rabbeinu Zerach) and the Milchemes (Ramban):
The 1st Mishna in Pesachim 4 (16b in the Rif) states that refraining from doing work on Nissan 14 before noon is based on the custom of the city. The Baal haMeor comments that the Mishna implies that work after noon is independent of custom and is strictly forbidden, quoting a Yerushalmi that the sages prohibited work during the time of korban. The Baal haMeor concludes that since nowadays there is no korban, work is not strictly forbidden and is based on custom.
The Ramban rejects the baal haMeor's conclusion, bringing supporting proofs, and concludes that the prohibition of work after noon remains.
Summary: There is a dispute whether work on the afternoon of Nissan 14 is rabinnically forbidden or if it is merely a custom. This would make a difference in whether or not vihi noam is said.