Can You Turn an Xbox 360 into a PS3?

Absolutely not. The Xbox 360 and PlayStation 3 are fundamentally different machines:

Aspect	Xbox 360	PlayStation 3
CPU	Triple-core PowerPC (Xenon)	Cell Broadband Engine (1 PPE + 7 SPEs)
GPU	ATI Xenos (Unified shaders)	NVIDIA RSX (Pixel/vertex split)
RAM	512 MB GDDR3 (unified)	256 MB XDR + 256 MB GDDR3 (split)
OS	Xbox Dashboard (NT-based)	CellOS / XMB (FreeBSD-derived)
Media	DVD-DL	Blu-ray

What You Can Do

Play PS3 games on PC via RPCS3 emulator (requires powerful CPU/GPU, legal game dumps).
Enjoy cross-platform titles (e.g., Call of Duty, Assassin's Creed, GTA V) on either console.
Upgrade: A used PS3 Super Slim (~$80–$120) or PS4/PS5 gives native access.

Hardware conversion is physically impossible—don't risk damaging your 360.

Xbox 360

Xbox 360