It's not power, it's bandwidth. The higher bandwidth you have, the faster risetimes you can measure. It's roughly analogous to the difference between a blurry cheap telescope with plastic optics and an expensive one with high quality coated glass optics, with the latter you can see more detail and a more accurate representation of what you are trying to look at. Cost rises very rapidly beyond about 100MHz bandwidth, both for scopes and the probes.
Honestly if you have never used an oscilloscope a TDS3000 is probably going to be a bit overwhelming, it's a bit like handing a new driver the keys to an expensive luxury car. Be sure to watch Dave's video on how to not blow up your oscilloscope, and never, ever be tempted to try poking around in mains powered equipment until you really know what you're doing. Watch that video, then watch some videos on how to use an oscilloscope, then read the manual, it can be downloaded for free. If you know someone who can walk you through using it that would also be very helpful. Take good care of it and it should serve you well for many years, the related TDS3054C is still available new and costs over $20k. These don't have the greatest memory depth by modern standards but the bandwidth they can offer blows away any of the hobbyist oriented scopes on the market which typically top out around 200MHz.
I cannot stress enough how important it is to know how to not blow it up, and do not subject the inputs to any signals beyond what they are rated to accept, use of a 10x probe is highly recommended and avoid using the 50 Ohm setting unless you know you need it for something because it's 5VRMS max. If you blow up an input the parts are unobtainium and you'll be looking at spending significantly more than you paid for the whole scope to get a replacement board if you can find one.