Yes, there is a trade-off. To get the same current out of higher resistance, you need higher voltage. Also, as you increase the resistance, keeping the current constant, you will develop more heat. This puts a practical limit to how small or how strong you can make particular electromagnets. There's also the issue of core saturation (maximum flux) to deal with. Different ferrites have different saturation points.
There are text books that talk about this in great detail. If you want to design electromagnets, I highly recommend getting one and reading it! This subject has been studied in great detail for anything from inductors, to transformers, to loudspeakers, to motors, to solenoids.