"...let alone play a decent game online on my ps3"
This is due to latency and not due to low speed internet. As in if you are continents away from the player or server hosting then there will be lag. If the host is close to you then Lag will be nominal.
Lag (online gaming) - Wikipedia, the free encyclopedia
Though yes without doubt we are in trouble if Ps3 games are not released on Ps4 for download and I would quite like playing my disc-based Ps3 titles on the Ps4. Imagine Red Dead Redemption and Mass Effect making use of 8Gb of ram, a high powered graphics card and eight cores; that would be a-okay. Faster framerates, no jittering and so on. Sadly I guess that's not happening but let's see what happens.