Depends - They could work well together or piss all over your expectations because it's largely going to be a matter of what IC's are in the sticks and if they are compatable with each other.
This is also why it's not a great idea to mix-n-match sets, some IC's really don't like being in the same system others may be in, it's all hit or miss when you try things that way.
If the Corsairs you have are working fine another set of those would be what to go for..... However Corsair is also infamous for changing what IC's in a model line, even if it's the same thing by it's specs and all else.
Even versions of the same thing (Such as Corsair Pro PC3200 2-2-2-5 v1.2 as an example) by name and model/spec between sets could be shown as being the same but could also have different IC's under the heatspreaders and that has been seen before from Corsair.
I've bought Corsair RAM since, well, as far back as I can remember - certainly TwinX days, possibly even before DDR2 was a thing. Reason for that was reputation at the time, and a 'lifetime' warranty. I haven't looked yet what the warranty policies are for the likes of Patriot, G-Skill or Crucial. In fact, the only time I had to return RAM was three returns of Crucial Ballistix (years ago, some bright orange CL4 DDR2 things - BL12864AA804.8FE5 according to the wrapper. Yes I'm a hoarder).
Since then I've had no issues with Corsair RAM, apart from the M2Z3200C16s initially not working under A-XMP. But I was expecting to have to dial in the RAM settings - it was like that before A-XMP/DOCP/XMP anyway. Right now those sticks are running happily at 3600C16 with slighly looser timings, but stable as far as I can test (HCI MemTest >1500%, Memtest86 boot disk no errors) so I'm happy enough.
You're right about the changing of the ICs of course. I looked online earlier to see what ICs people had in their 3600C16 and 3600C18 sticks, and it varies between Hynix AFR, CJR, Samsung non-B, and Nanya - going by review comments and images people have posted.
If I want to get more RAM it seems like there's no guarantee that their ICs will match any more than another brand's sticks would, so I'll look at those next.