Only Chasidim Are Allowed

             (HALACHA V'LO L'MA'ASEH)

The Rema (O.Ch. 551: 1) writes, "On Shabbos Chazon 

one  must wear weekday clothes" (except the shirt)

The Aruch Hashulchan (551: 11)  writes ,"today we do 

change into Bigdei Shabbos. They were Matir wearing  

Bigdei Shabbos, otherwise, you  will be showing 

אבילות בפרהסיא(public) on Shabbos .

The Rema, he too knew of the issur of אבילות בפרהסיא ,  

yet he   wouldn’t  allow wearing Bigdei Shabbos

because, in the times of the Rema the style of dress 

between Shabbos  and weekday  was similar. 

By wearing weekday clothes there was no.אבילות בפרהסיא

It was only after they started wearing Bekeshes and Shtreimels 

on Shabbos,  were they  Matir wearing Bigdei Shabbos  

otherwise, it would be אבילות בפרהסיא" .

According to the A.H. ,the Heter of wearing Bigdei Shabbos 

is only for Chasidim who wear on Shabbos Shtreimels 

and Bekeshes and by not wearing them on Shabbos

it would be אבילות בפרהסיא
Those who wear suits  and hats on Shabbos would need to 

wear their weekday suit  and hat.

In Vilna, the Minhag was to follow the Gaon's Psak
and they wore Bigdei Shabbos.(Chaya Adam)

I am not sure if the Psak of the Gaon was only
for when they still had unique Shabbos Begodim
or even after they changed to modern clothing.