I was at DLR this past January 10 & 11. Park hours were shorter (DCA 10-8, DL 10-8) but crowds were perfect!! We barely even used FP because lines were that short. We got almost all the main big rides done before our first day was even over. The weather was amazing too. Only things that I didn't like were no fireworks or parades, WOC was showing though. Haunted Mansion was closed to remove the holiday overlay but It's a Small World was still open with the holiday overlay so it was cool to experience that. Overall, my trip in January was my favorite so far. Weather can be hit or miss though. A few days before, it was raining and the grapevine was closed due to snow. We just got lucky.
Now, I have never been in April, but I did just get back from DLR so I have experienced Spring Break crowds. Depending on when in April you wanna go and if that coincides with Spring break would be a major factor. It was super busy this past week! A CM told me this was the beginning of spring break for lots of people. Lines were 45-85 minutes for the most part. FP was running out by 3 for rides like Tower of Terror and Space Mountain. There were longer park hours (DCA 10-10, DLR 8-midnight) and fireworks. Only rides that were closed that aren't going through major updates (so, excluding goofy's sky school and star tours) was Splash Mountain. Rides were breaking down all day though

That probably has nothing to do with the time of year, but it wasn't fun waiting almost 60mins for Space Mountain just to reach the part of the line where you are almost inside the building and be told the ride was down. Also down at times were Indiana Jones and Big Thunder Mountain. Weather was great though!
Financially I don't think there is a difference with DLR tickets. Even with shorter park hours the ticket price is the same as when the park hours are longer. But lots of hotels have cheaper rates in January than during Spring Break season. For my January stay, we were at the Ramada Maingate which is right across the street from DLR. We used my friends corporate discount plus my
AAA discount and for 3 nights we paid less than $200. For my recent Spring Break season visit, we stayed at Castle Inn, which is still across the street from DLR but a bit of a further walk than the Ramada. We paid about $258 for 3 nights, and that was after spending lots of time online searching for good deals.
Hopefully my experiences have helped a little bit in your planning. For me, I would pick January. I loved how uncrowded it was! I had never experienced such short lines and uncrowded walkways were sooo nice! But the weather is tricky in January.