Some History - When Office365 first came out, it was available only via online purchase. Microsoft resellers who wanted to resell office365 needed to be registered for that business model and they get compensated via rebates. This new sales model resulted in a number of issues (which I will not mention here). As a result of these issues, Microsoft now offers an alternative purchase method for Office365 via Open Licenses.
O365 via Open Licenses is more restrictive as compared to buying online. They require a one year purchase, the subscription end dates moves as you add licenses. The licenses are not refundable if cancelled..etc. Also, you don't get to add licenses on the fly. You have to ask for your usual 3 quotes, negotiate, place an order with the partner, then the partner places an order with the distributor, and the distributor with Microsoft, and wait for Microsoft to generate the license for you.
O365 via Online, on the other hand, allows you to pay by month, the subscription end dates stay the same even when you add new licenses (Microsoft just adds the amount to next month's bill), you get a 30 day penalty for cancellation (rather than not being able to get a refund), you can add licenses on the fly..etc.
Now, for your partner. If your partner is a registered Office365 Online partner (which usually means they were doing Office365 much earlier on and is a "Office365 focused partner" as compared to a Microsoft reseller that can re-sell all licenses), this would not matter to them as they get recognized all the same for their effort. In this case, you can switch your licenses to online and continue on with life.
If your partner is a regular Microsoft reseller and simply gets a quote from a distributor and marks up, then purchasing online with Microsoft means he doesnt get compensated for the licenses. You can find another partner who does, or you can stick with this partner but he doesnt get recognized for online licenses if you decide to go that path.
One possible benefit of purchasing through a partner is the difference in prices. The Microsoft Online Portal prices are pretty fixed. However, the partner may be willing to offer you a cheaper price as Open licenses are quoted to you as dealer cost + dealer markup. Also depending on what products the local microsoft office is not doing well in, they might be having certain promotions for O365 Open License which ends up being cheaper than the Online price.
Hope this fills the gap to your question. Whatever you decide to do, June is probably the best month to discuss with Microsoft as its their financial year closing.