This was actually my first instinct too, here was the output I got from testing with B::Concise.

stvn% perl -MO=Concise -e '$x++'
5  <@> leave[1 ref] vKP/REFC ->(end)
1     <0> enter ->2
2     <;> nextstate(main 1 -e:1) v ->3
4     <1> preinc[t2] vK/1 ->5
-        <1> ex-rv2sv sKRM/1 ->4
3           <#> gvsv[*x] s ->4
-e syntax OK
stvn% perl -MO=Concise -e '$x += 1'
6  <@> leave[1 ref] vKP/REFC ->(end)
1     <0> enter ->2
2     <;> nextstate(main 1 -e:1) v ->3
5     <2> add[t2] vKS/2 ->6
-        <1> ex-rv2sv sKRM/1 ->4
3           <#> gvsv[*x] s ->4
4        <$> const[IV 1] s ->5
-e syntax OK
stvn% perl -MO=Concise -e '$x = $x + 1'
8  <@> leave[1 ref] vKP/REFC ->(end)
1     <0> enter ->2
2     <;> nextstate(main 1 -e:1) v ->3
7     <2> sassign vKS/2 ->8
5        <2> add[t3] sK/2 ->6
-           <1> ex-rv2sv sK/1 ->4
3              <#> gvsv[*x] s ->4
4           <$> const[IV 1] s ->5
-        <1> ex-rv2sv sKRM*/1 ->7
6           <#> gvsv[*x] s ->7
-e syntax OK
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You can see that the x += 1 and x = x + 1 are similar, but not enough to call equivalent. Besides I am not sure that opcode equivalence would actually work since perl performs optimizations on the opcode tree during compilation which you would not want to include in your comparisons.