Not all pins are created equal. On the 16F628 RA0 and RA1 are ST "Schmitt Trigger"
type buffers.

If the RX pin isn't seeing 0.8 * Vdd (around 4V with Vdd = 5), it wont see high enough
signal levels when receiving serial data. This can also be affected by external capacitance.

I.E. even with a TTL type input, external capacitance on the pin can degrade the serial
data to where it fails.

One the16F876A RA0 and RA1 are TTL buffer types, and the incoming signal only needs to
swing from ~2V to ground.

For reliability, like mister_e already mentioned, you definitely should go with a >4MHz osc
if you're using 9600 or greater.