Taking off catalytic converters will increase performance by allowing fumes to escape faster. You will also get a huge increase of sound, in my opinion I love the sound of a cat-less V8, especially mustangs.
Taking your catalytic converters off is ILLEGAL. There are actually strict laws, but never really enforced.
Your check engine
light will come on.
You'll smell the fumes from the exhaust. ( a tune will reduce this a lot)
You won't be able to pass emissions. Especially if they have a sniffer.
A SCT tuner can turn off the CEL
There are also plugs that trick your O2 sensors into thinking they are hooked up to cats
If you got the $$ and a trustworthy hook up.. It's possible to pass emissions, but it's still illegally done.
What also some people do is save their OEM Midpipe and every inspection just swap the cats back on.