I personally don't believe it is that hard replacing the PSU because I have done it quit a few times. With that 550w modular one it should be pretty easy. Your HDD have one SATA power connector along with the Optical drives. Your motherboard has one main connector (20/24 pin connector) and another one for your CPU cooler fan (4/8 pin connector). Depending on your case you may also have some fans connected to the PSU by molex/peripheral connectors. Lastly the GPU will have one or two (one for 7850 two for 7870) PCI-E connectors.
You can decide if you think the 7870 is worth the increase in price over the 7850. The 7870 performs close to the 580 and the 7850 performs similar to the 570.http://www.tomshardware.com/reviews/radeon-hd-7870-review-benchmark,3148.html