OK, it is a question of what the connection polynomial is, the figure helps clarify what you are doing. In both cases the polynomial is degree 8.
Originally, your connection polynomial is
$1+x+x^4+x^5+x^6+x^8$ (I wrote it in the order of the LFSR connections). This polynomial is not primitive, it's not even irreducible, with the factorization
$$
1+x+x^4+x^5+x^6+x^8=(x+1)^2(x^4+x^3+1)(x^2 + x + 1)
$$
so there is no question of obtaining the full period of $2^\text{degree}-1=2^8-1$ from it. Depending on the loading it will give shorter periods but never full period. See this question Non primitive lfsr sequence for more info on what periods are possible.
When you change the connection you have the polynomial
$1+x^4+x^5+x^6+x^8$ which has no factorisation into a product of lower degree polynomials (so it is irreducible). This polynomial is actually primitive and will give a maximum possible length sequence with period $2^8-1.$
See also Wikipedia here. I have used the following commands on Magma to check these properties.
R:=PolynomialRing(GF(2));
f:=1+x+x^4+x^5+x^6+x^8;
IsPrimitive(f);
Factorisation(f);
f:=1+x^4+x^5+x^6+x^8;
IsPrimitive(f);
Factorisation(f);
with output
false
[
<x + 1, 2>,
<x^2 + x + 1, 1>,
<x^4 + x^3 + 1, 1>
]
true
[
<x^8 + x^6 + x^5 + x^4 + 1, 1>
]
Gadiel Seroussi has given a very long list of primitive polynomials up to degree 10,000 here.
