They both make a difference. You need to be careful when asking for opinions like this. Most people get their listening experience by reading spec sheets and reviews. Or they just guess because they think they know better. For example, someone that strongly recommends a dac instead of a transport may think a transport can't make a difference. And if it does, something is broken. Most of the time, people with views like this have absolutely no experience with anything they're talking about. They just think they know. Upgrading your audio system is a hands on process. If you let other people make the decision for you, don't expect to be happy.
If you decide to go with separates, you still have to match the transport to the dac, just like you would an amp and preamp. If you're mixing brands, I would want to listen to both pieces together. For just listening to CD's, I would buy a Redbook only player. Its a cleaner solution. One box, and you know everything is going to work well together. With a multiformat player like your Oppo, it has to start up and load its operating system. The functions usually work a lot slower. A CD player is just nicer to use. Just to be clear, I'm not saying you can't get great sound from separates. You can. I'm just giving you my preference.
There's one product that comes to mind that you may want to look at. Rotel makes what they call a transport with a dac. Yes, its another way of saying its a CD player. Most CD players just have a digital out, but not much thought was given to using it as a transport. If you get the Audiolab transport, you should notice a respectable difference over your Oppo's transport. I would expect to get the same level of transport upgrade with the Rotel. However, you may be perfectly happy with the dac in the Rotel, as well. Rotel digital products have always been very hard to beat for the money. I don't think its that much more than the Audiolab. If you then decide to upgrade your dac later, you have a CD player that was designed to be used as a transport only.