c4, d4 vs c5, d5: what to do?

The engine "usually" indicates cxd not the other one... but of course many times dxc is good.

I've made very long posts about this in the past, but I guess if I tried to answer in a few sentences it would be...

Play cxd to open the c file.

Play dxc to open your g2 bishop / the d file.

Either way, by capturing first you will avoid being the owner of an IQP or hanging pawns structure... you might give your opponent an IQP or hanging pawns structure if they recapture with pawns.

Either way you capture, it's usually better to wait until late in the opening as an early pawn trade will give your opponent more development options. For example cxd exd will remove their e pawn and so possibly open up a bishop. cxd cxd removes their c pawn and may open up a square for their knight.

If you play both captures, and they recapture with a piece both times, (meaning not a pawn) then it can be pretty drawish / boring (if development is close to equal).

usually leads to a few typical pawn structures, iqp, hanging pawns, symmetrical with open c and d file. you ought to see the ideal piece placement and typical plans for both sides so that when something is off for one side or the other then you go for the structure that gives you that advantage.

for instance, against a knight on c3/c6, there is this idea of dxc5/dxc4 followed by a3 and b4 or a6 and b5, given that at some point b4-b5 or b5-b4 will kick that knight with tempo, leaving e4/e5 one defender less.

and in iqp positions you usually don't want the kb to obstruct the queen's path to defending the d-pawn so if you see bd3/bd6 and can convert to an iqp you should have a better version of it. another consequence is that the pin with bg5/bg4 is more annoying.

so things like that.