Resolution not power is what is important to see detail on planets. That and good contrast. In approximate terms a 4" scope will be able to resolve 1" of arc detail. But this is very misleading in some ways. A linear feature of high contrast that is much smaller than 1" of arc can be seen in such a scope, such as Cassini's division in the rings. That is about a half second of arc at its widest point but a 4" scope will show it quite clearly not only where it is widest but even a lot narrower than that. But detail in Jupiter's cloud belts requires a telescope that gives high contrast as well as good resolution. A photo is misleading because the imager can boost the contrast far beyond what the human eye sees. While a Newtonian and a refractor of the same size will have the same resolution you will see more in the refractor because it's contrast in higher. This is due to it not having a central obstruction. So to see the same low contrast detail you need a reflector about 50% larger than a refractor that just shows this detail. This is a very general statement. A long focal length newtonian with a very small secondary obstruction can come close to refractor performance. My home built (mirror included) 6" f/12 with half inch secondary equals any 5" apo refractor I've looked through. Of course Newtonians (especially Dobsonian mounted ones) are far cheaper than an equivalent refractor. Right now my planetarium program tells me Jupiter is 32" of arc across while Saturn is 17" though the rings are 41" across. A 60mm refractor or 3" reflector will show Jupiter and Saturn with its rings very nicely but to see detail on Saturn's disk or in Jupiter's bands you will need a 4" refractor or 6" to 8" Newtonian.
Back to that 4" objective giving 1" resolution, if you double that to 8" then you have 0.5" resolution IF the atmosphere allows it. By 8" you are starting to put some pressure on the atmosphere to deliver a steady image. Much above this aperture you'll gain little resolution but contrast at should continue to increase meaning even though you don't see finer detail of high contrast you do see a lot more finer detail of low contrast. The appearance is you are seeing a lot more detail over all. A imager however will likely see little difference after he's pushed the contrast to optimum levels. Now if you are on Kitt Peak or other location with better than average seeing then larger aperture will greatly improve the view. Where I live that's sadly not the case.
In other words you soon get aperture fever until the scope is so big it literally breaks your back to carry it.
You need to get to that star party I mentioned and actually look through a bunch of scopes to get an idea of what all this means. I can type on and on but as they say one star party is worth 10,000 posts here for what you will learn and really start to understand.
The link below will locate a club near you. Don't even think of buying a first scope without going to one and learning what you really see through the various types and sizes of scopes. Actually your first scope should be a pair of binoculars. They are half way in light gathering ability and resolution of your eye and a 13.5" telescope! No amateur astronomer would ever leave his house for star gazing without them. See Dave's post on binoculars. This is a lot more important than you can imagine.
http://www.skyandtelescope.com/community/organizations
Aurora has already told you why I never mentioned power in this post. Power tells you little to nothing about what you'll see in the scope. That's determined by its quality and aperture and our atmosphere. I could take any telescope to any power you mention, even one million. It won't help you to see anything, except a virtual black hole, but it can be done.
In fact power can be your enemy. For instance a galaxy will be 25 times brighter at 20x in a 4" scope than at 100x. Since they are faint to start with you will likely see far more at 20x than at 100x and certainly far more than at 200x which is where the image starts to break down from being enlarged too much, same as a photo or your TV screen. But since everything is really dim anyway it hardly matters it is fuzzy too.
Rick