A really BIG question....
Contact implementation partners for SAP and JDE to ask for their help in evaluating the products (eg, Deloitte & Touche in Germany has a tool to compare these 2 products). Remember they have their agenda (like an SAP implementation will employ a lot more people for a longer time than will a JDE implementation).
If you can, talk to the day-to-day people who were on the implementation team for each of the products to get a sense of the project issues -- good and bad. And also ask for a "working system" demonstration of business processes that your company will use so the team members can actually "touch and feel" both products. Make sure the integration is demonstrated so team members have a sense of how important their efforts are to the success of the project (eg, process a sales order and a purchase order to see inventory changes and the updates to accounting, then have the customer pay you and you pay your vendor).
In the end, good, knowledgeable people are needed to make a successful implementation and most of those people must come from your company. The implementation partners primary goal should be to make you independent from them.
Finally, remember far less money is spent in the early stages of the project than in the later stages and after Go Live, so planning (eg, doing things like business process modeling) is "cheap" compared to mid-implementation crisis management. Know what you are doing BEFORE you jump into the implmentation.
and GOOD LUCK whatever you choose.