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If you're using a mech (or other fixed voltage device) then the resistance is what defines the power:

watts = volts^2/ohms

So resistance makes a huge difference with fixed voltage batteries. Before the advent of high power regulated mods, mechs with low resistance were the only way to get high power, so people used to (and to some extent still do) use resistance as an alternative measure of power.

These days we have high power regulated mods and resistance matters much less because you can change the voltage to get the power output you want. It still matters - if you have a maximum of 6v then the maximum power with 2ohms is 18w, with 1ohm 36w, etc. But you don't have to target resistance as precisely to get the power you want.

It will still make a difference in other ways. If you have a 2ohm coil and want to make a 1ohm coil instead, you probably don't want to halve the number of wraps, so you will end up using thicker wire. If you keep the power the same, it will take longer to heat up - which will give a smoother vape if your 2ohm coil was a bit harsh, or will be sluggish and eat battery life if your 2ohm coil was about right.

Probably the best approach is to decide your target resistance (or target range of resistances) - which will depend on the power you want to vape at and the battery you want to use - and then find a coil build that hits that whilst giving you a coil large enough to take the power (and small enough to heat up rapidly at that power).

www.steam-engine.org/coil.asp is handy for this. The heat flux calculation at the bottom will help you work out if a build is likely to work well at your preferred power. mW/mm2 needs to be somewhere between 150 and 350 - which part of that range works best depends on your attie (faster juice supply and higher air flow will both cool the coil more) and your juice (some flavours are better at lower/higher temperatures) and your vaping style (long draws will reach higher temps than short ones, as will chain vaping).

If you have some builds that work well for you in a particular attie, plug them into steam-engine to get an idea of the sort of heat flux you should probably be aiming for with a different build.

You can play around with twisted/parallel builds, or lower resistance wires (nichrome, stainless steel) to get quicker heat up times on big coils - thinner wire is less sluggish. Thicker wire will be smoother. There's no right answer - just a lot of variables you can play with to get what you want.