But looking up the specs on a 4770, there are a few things you should know. This may sound ridiculous, but I've checked the specs twice. The 4770 was ahead of it's time. It was built on a 40 nanometer process. After 40nm came 28nm(today's tech). So even though it's branded a 4XXX series card, it's really only a generation behind. Radeon 5XXX and 6XXX were all 40nm as well. All the other 4XXX series cards were 55nm(2 generations ago).
What you really need to know it's it's graphical power. A 4770 is rated at 960 gigaflops and uses 80 watts of power(max). A Radeon 7850 is rated at 1761 gigaflops and uses 130 watts. So if you get a 7850 it will be an improvement; although not even double! You'll need a Radeon 7870 to put that 4770 to bed. The 7870 is rated at 2560 gigaflops However, it needs 175 watts. So your PSU must have two 6 power connectors.
If you were to crossfire a 4770, I "wouldn't blame you". However there are also other considerations. Direct X would be one. The current standard is 11.1 and most new games are 11.0 The 4470 only support 10.1, so you would be missing some modern effects. And then there is heat issues (dust get baked on over time) and just the age of the card in general. Driver support for modern games is likely lacking.
The 4770 was released in April of 2009. And if you've had yours for years, it paid for itself long ago!