Compared to Tokyo Station,
Shinagawa Station of JR is smaller and much simpler;
for a passenger
who has reserved his/her seat
for his/her Tokaido Shinkansen train ride,
Shinagawa Station sounds more suitable
to make a transfer to the Shinkansen,
especially when he/she gets to Tokyo on a Narita Express train.
In Shinagawa Station,
there is only one Shinkansen zone,
which is for Tokaido Shinkansen;
disembarking from your non-JR train,
you can just find and follow signs for Shinkansen
then reach a correct Shinkansen gate. http://english.jr-central.co.jp/info/station/_img/shinagawa_L.jpg
In Tokyo Station,
there are two separate Shinkansen zones;
different gates or entrances | exits
which are close to each other
have a same or similar name,
in a few cases;
so as not to mistake
a gate of the other Shinkansen zone as your gate,
you carefully follow sings for Tokaido and Sanyo Shinkansen. http://english.jr-central.co.jp/info/station/_img/tokyo_L.jpg
: Westbound Tokaido Shinkansen trains
leave for the left in the above-link Shinagawa Station's map,
leave for the right in the above-link Tokyo Station's map.
When you choose Tokyo Station
to make your transfer to the Shinkansen,
I recommend you also look at pictograms representing Shinkansen.
(A) Blue-and-white pictograms are used
for Tokaido and Sanyo Shinkansen.
: Example: https://www.japan-guide.com/g3/2018_how_sign.jpg
(B) Green-and-white pictograms are used
for Tohoku, Joetsu and Hokuriku Shinkansen.
On the front side of your Smart-Ex ticket,
the station from which you take the Shinkansen train
is indicated probably just as Tokyo Station;
when you choose Shinagawa Station,
you renew the Smart-Ex ticket in advance of your train ride.