Hi and welcome.
Well, let me take a shot at this. Bot DNA is actually a little more complex than a sequence of integers. It's actually made up of a sequence of typed values. Think of it as a string of pairs of numbers where one number is the type and one is the value. The textual DNA that humans author or the program displays or saves is a tokenized version of this underlying sequence of type-value pairs. So, when a human writes something like:
cond
*.nrg 100 >
start
10 .up store
stop
it gets represented inside the program as:
9 1
1 310
0 100
5 2
9 2
0 10
1 1
7 1
9 4
10 1
That is the actual underlying type-value representation of the gene above. That last pair (10 1) is the "end" base pair. (For historical reasons, we use the term "base pair" to refer to a type-value pair but the term "codon" might actually be a better analogy.)
Anyway, the mutation code knows to only mutate to type-value pairs in the defined genome space. For example, there are only four values in the space of the "flow control" type (type 9): cond, start, else and stop. These are represented interally as:
9 1
9 2
9 3
9 4
Thus, the mutation code will never mutate to a 9 5 for example. The simulator code prevents this. But it might mutate to a 0 31987 since the "0" type is the space of all integers -32000 -> 32000 inclusive.
Given this and the way the DNA "language" works, there is no such thing as an invalid genome. A mutation may break or radically change some functionality, but every genome in the space of all posible genomes are "valid" in the sense that the simulator will handle them just fine. A particular sequence may not do anything interesting - indeed most probalby do not as the morphospace is vast - but they will exectue and certainly won't cause problems for the simulator.
What the different mutation types actaully do to the genome depends (not surprisingly) on the type of the mutation. Point mutations change a single base pair for example. A sequence copy mutation duplicates a sequence of base pairs. FYI, no mutation type respects gene boundaries.
So, to answer your question, if you compared two homologous genomes in a txt editor, you would see a different sequence of base pairs - the tokenized representations of the underlying type-value base pair sequences - and not a rearrangement of genes. Since no mutation type respects gene structure, preservation of gene structure is a strong sign of conserving selection pressure or perhaps an indication of horizontal gene flow via viral infection.
If you want more detail, ask away.
Generally speaking, you'll see numbers and words changed around, some gene structure changes, etc. Genes shouldn't be rearranged without viral propagation or somesuch.
Man, I got to get me some brevity...