E vs A country (mixolydian) thirds — B (2nd) & G (3rd) strings

Flat-7 scales — the country sound. Most shapes transfer directly between E and A. Only two pairs actually differ.

E country only
A country only
Shared by both
Root
The shortcut: with the flat-7 (mixolydian), the only note that differs between E country and A country is G# (E's 3rd) vs G (A's b7). Everywhere else the scales agree. So 5 of your 7 third-shapes on strings 2 & 3 are identical between the two keys — memorize once, use in both.

Scales

E country (E mixolydian) = E F# G# A B C# D
A country (A mixolydian) = A B C# D E F# G
The single note of difference is G# (in E, not A) vs G (in A, not E).

Diatonic thirds on strings 3 (G) & 2 (B)

Pair (low → high) Interval G-string fret B-string fret Shape In E? In A?
A–C#major 3rd2 / 142 / 14same fretyesyes
B–Dminor 3rd43split (G higher)yesyes
C#–Eminor 3rd65split (G higher)yesyes
D–F#major 3rd77same fretyesyes
F#–Aminor 3rd1110split (G higher)yesyes
E–G#major 3rd99same fretyes (E only)
E–Gminor 3rd98split (G higher)yes (A only)
G#–Bminor 3rd1 / 130 / 12split (G higher)yes (E only)
G–Bmajor 3rd0 / 120 / 12same fretyes (A only)

Where the two keys actually differ

Two fret regions. Everything else is the same.

Around fret 9 (the E position):
E country: E–G# on fret 9 of both strings — same-fret major 3rd.
A country: E–G on G:9 / B:8 — split minor 3rd.
Same root note (E), different upper note, different shape.

Around the nut / fret 12 (the open position):
E country: G#–B on G:1 / B:0 (or G:13 / B:12) — split minor 3rd.
A country: G–B on open/open (or fret 12 / 12) — same-fret major 3rd.

Pattern to hear: the two "flip" pairs always swap shapes. If a shape is "same-fret" in E, it's "split" in A at that same scale position — and vice versa. That's literally the one-note difference (G# ↔ G) expressing itself as a shape change.