The downside is moving the CG forward. This is particularly important when lightly loaded. Cessna put the battery back there for a reason.
A firewall mounted Odyssey was installed on my 180 by a previous owner close to 20 years ago.
They did some other stuff at the same time, but when I crunch the numbers from their W&B revision,
it looks like the battery mod resulted in 14 pounds less weight and moved the CG forward 1.9".
This 180 has had a fairly forward CG since I've owned it (currently at 34.6" empty),
it's the only one I have any time in to speak of, but it flies fine.
No problem flaring, even with full flaps, which I've heard is sometimes a problem.
A more aft CG might give it snappier handling, and would probably result in slightly higher cruise speed & slightly lower stall speed--
but on the positive side, the forward CG allows you to carry more gear in back while still staying in the CG envelope.
I like that there's not several feet of battery cable to add weight & voltage loss.
All in all, I'd say the pluses outweigh the minuses.