Does the PS4 Make the PS3 Obsolete? No—PS3 Retains Unique Value

No. The PS3 retains unique value the PS4 cannot replace.

PS3 Exclusive Advantages

Native PS2 Backward Compatibility: Launch 60GB/20GB (NTSC) & 60GB (PAL) play PS2 discs directly (Hardware Emotion Engine + Graphics Synthesizer). PS4: Zero disc BC.
PS1 Disc Playback: All PS3s play PS1 discs. PS4: None.
Media Server / DLNA: PS3 is a superb DLNA renderer (PS3 Media Server, Universal Media Server). Plays MKV, ISO, FLAC, ASS subs from NAS/PC. PS4 Media Player is limited.
Linux / OtherOS (Fat only, FW ≤3.21): Historical/homebrew value.
Sacred Exclusives: MGS4, Demon's Souls (Original), MGS Legacy Collection, Yakuza 1/2 HD, Folklore, 3D Dot Game Heroes, Puppeteer, The Last Guy, Ni no Kuni (DS/PS3), White Knight Chronicles. Not on PS4/PS5.
Blu-ray 3D Playback: PS3 supports. PS4 removed.
Price: $50–$100 used. Cheap Blu-ray/Retro station.

PS4 Advantages

Modern games (2013–2024), 1080p/60fps standard, Remote Play (PC/Phone/Vita), Share button, Party Chat, Suspend/Resume, PSVR, Pro (4K checkerboard).

Verdict

Keep both. PS3 = Retro library (PS1/PS2/PS3 exclusives) + Media Server. PS4 = Modern library + QoL. If space/money forces one: PS4 for new games; PS3 for history/media.

PS3 Games