I'm not familiar with Shareowners. I guess the question I would have would be what fees are involved in both locations. There will certainly be a fee to sell, but what about buying? Also, is there something you can do with one and not the other? For instance, one of the nice things about a DRiP is that you can send $100 and buy $100 in stock, whereas with a discount broker you need to make purchases in whole shares. (On the other hand, getting set up with a traditional DRiP is time-consuming and there can be fees involved.)
If all things are equal then I would simply build a new portfolio with Shareowners. The only downside is that you have an additional form to deal with when it comes tax time, but that sort of thing has never really been an issue for me personally.