I've just done this and give from Cobra to DBX. Depending on configuration you're going to be down about 8 tons of cargo space. It can't boost away from trouble as easy and it didn't pitch as well.
On the plus side it's energy mgt is very good and it has 2x med 1x large which means you can give it a decent sting for those intercepting. It's shields aren't as strong but you can fit 4x utility so a couple of A0 shield boosters help. Hull is very tough as standard and can take a pounding. Biggest thing I'd that jump range is superior to Cobra.
Personally, I gave it a go as I was wanting a bit more firepower than Cobra could deliver, but its a real tank so not ideal as a multi role ship.
I'm considering getting a DBS (which is awesome for BH) and a Type 6 for trading. DBX is just not really value for money, although it is interesting.