Convert from AVI to MP4: Best Settings?

Your source file’s refresh rate is 50 Hz because it is interlaced. When you output the H.264 MP4, you chose progressive (not interlaced), which gave you 25 Hz because it is 25 fps. This will impair motion. Shotcut is not able to deinterlace in a manner that up-samples the frame rate. You can choose set Shotcut Export > Video > Scan mode to Interlaced to preserve the interlace - even for H.264 MP4.